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THE 



PRINCIPLES OF LOGIC 



BY 



HERBERT AUSTIN AlKINS, Ph.D. 

Leffingwell Professor of Philosophy in the College for Women of 
Western Reserve University 




NEW YORK 

HENRY HOLT AND COMPANY 

1902 



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'^^. ' li 



THE IJBRAWY ®F 
eONGR&SS, 

Two <50PJE8 Receive* 

APR. t9 1902 

COFYRIQMT ENTRY 

CkAss«.'XXa N®. 

S /^ i ^ 



Copyright, 1902, 

BY 

HENRY HOLT & CO. 



ROBERT DRUMMOND, PRINTER, NEW YORK 






PREFACE. 

The deductive part of this book may require a few words 
of explanation. 

In most text-books on logic deduction and induction are 
treated from two very different standpoints. Induction is 
regarded as a means for the investigation of nature, and its 
canons are frankly objective or ' material '. They tell us 
how things must be related to each other in one respect if 
they are also related in some other respect {e.g., how two 
events must be related in time if one is the cause of the 
other) ; and they do not say anything about the relation of 
our thoughts to each other as mere thoughts, or give any 
rules for the arrangement and manipulation of the words in 
which these thoughts are expressed. 

Deduction, on the other hand, is usually defined as the 
** science of the laws of thought'' — as one writer says, its 
*' object-matter is thought'', — and it is treated altogether 
from the subjective or ' formal ' standpoint, as though mere 
thoughts as such could be consistent or inconsistent, wholly 
regardless of the nature of the object to which they refer; 
and then, when it comes to working out the details of the 
subject from this standpoint, the ' laws of thought ' are 
treated practically as though they were laws for the right 
arrangement and manipulation of words. Hence we have 
rules of the syllogism and allied rules for conversion and 
obversion which say nothing whatever about the things 
under discussion and their relations to each other, but tell 
us only how we must or must not arrange our words in dis- 
cussing them. 

iii 



IV PREFACE. 

In this book I have tried to treat deduction from the 
objective standpoint that everybody assumes in the treatment 
of induction. Consequently I have omitted the traditional 
rules of the syllogism and put in their place a direct state- 
ment of the principles on which we reason in the different 
figures, adding certain ' cautions ' that must be observed if 
the principles are not to be misapplied; and I have treated 
conversion and obversion in much the same way. 

The fourth figure of the syllogism seemed to me not to 
represent any distinct principle of reasoning, and therefore 
to have no proper place in the objective treatment of logic; 
but I have explained the traditional way of dealing with it. 
The * algebra ' of logic I have omitted altogether. Readers 
interested in it are referred to the ** Johns Hopkins Studies 
in Logic'' (Little, Brown & Co., Boston). 

However imperfect my own treatment of deduction from 
the objective standpoint may be, I believe that the stand- 
point itself is not only more correct philosophically than the 
subjective, but also better pedagogically; for we do far more 
to make a student clear-headed by teaching him to look a 
situation in the face and analyze it than by giving him any 
amount of dexterity in the reduction of arguments to a given 
verbal form. 

My indebtedness to other authors is apparent. I am no 
less indebted to individuals — particularly to colleagues in 
other departments who have given me valuable suggestions 
on matters related to their special subjects; but most of all 
to Dr. W. T. Marvin, to whom I read the whole book while 
it was still in manuscript. 

H. A. A. 

March 21, 1902, 



CONTENTS. 



CHAPTER I.— Introduction. 

Two kinds of thinking, i — ^Judgments and propositions, 2 — A dif- 
ferent view of judgments, 4 — Logical thinking is objective, 6 — Scope 
of logic^ 6 — Truth impersonal, 7 — Corollary, 9 — Fact and feel- 
ing, 10. 

CHAPTER n.— The Meanings of Words. 

Blunders of interpretation, 13 — How words become ambiguous, 16 — 
What ambiguities are most dangerous, 17 — Blunders of inference, 
22 — Paronymous terms, 28 — How to deal with ambiguities, 29 — 
Definition, 30 — How to frame definitions, 31 — Illustrations, 32 — 
Where precision is needed most, 34. 

CHAPTER in. — The Meaning of Statements as a 

Whole. 

Conventional phrases, 36 — Oblique senses, 37 — Exaggeration, 38 — 
Amphibology, 39 — Accident, 39 — Accent, 42. 

CHAPTER IV. — Division and Classification. 

Relation to definition, 45— Principles of division and subdivision, 45— 
Cross-division, 47 — Some technical names, 50 — Scientific classifica- 
tion and its purposes, 50 — Naming, 55. 

CHAPTER v.— The Uses of Single Words and Phrases. 

Terms, 56 — Demonstrative and descriptive, 58 — Connotative and 
non-connotative, 60 — Singular and general, 61 — Epithets, 62 — Col- 
lective and distributive, 63— The danger, 64 — Abstract and con- 

V 



VI CONTENTS. 

Crete, 65 — Hypostatising abstractions, 66 — Secondary meaning of 
'abstract*, 70 — Positive and negative, 71 — Relative and absolute : 
first sense, 73 — Second sense, 74— Dangers, 75. 

CHAPTER VI. — The Relations Expressed in 
Propositions. 

Five fundamental relations, 77 — Certain combined relations, 84. 

CHAPTER VH. — What Propositions Imply about 

Existence. 

The two * subjects ', 87 — Denials of relations and of existence, 89 — 
The conception of reality, 91. 

CHAPTER Vni. — The Formal Characteristics of 

Propositions. 

Quantity and quality, 96 — Ambiguities of quantity and quality, 98 — 
Undesignated quantity or quality, 99 — Double quantity, 102 — 
Exclusives and exceptives, 103 — Disjunctives and hypotheticals, 106. 

CHAPTER IX. — The Opposition of Propositions. 

With common propositions, 11 1 — With exclusives and exceptives, 
115 — Symbols, 117. 

CHAPTER X. — Inference and the so-called Laws of 

Thought. 

Inference — what, 121 — Deduction, 122 — The three 'Laws of 
Thought', 124— Obversion, 130. 

CHAPTER XL — Immediate Inference, or Inference 
FROM A Single Premise. 

Conversion, 131 — The traditional treatment, 132 — The treatment by 
diagrams, 140 — A broader treatment, 142. 

CHAPTER XII. — Mediate Inference and Syllogism. 

Limitations of deduction, 145 — 'Figures', 148. 



CONTENTS. vii 

CHAPTER XIII. — The First Figure of the Syllogism. 

General function, 150 — Is there real inference? 152 — Principle 
and cautions, 155. 

CHAPTER XIV. — The Second Figure of the Syllogism. 

Function and general cautions, 162 — Quantity in the second figure, 
167. 

CHAPTER XV. — The Third Figure of the Syllogism. 

Purpose, principle, and general caution, 171 — Negative relations, 
174 — Quantity of the premises, 175. 

CHAPTER XVI.— The Alleged Fourth Figure. 

Origin of the figure, 176 — Three ways of dealing with it, 176 — For- 
mal reduction, 178. 

CHAPTER XVII. — Other Deductive Arguments. 

Hypothetical syllogisms, 183 — Disjunctive syllogisms, 186 — Dilem- 
mas, 186 — Three forms of abbreviated argument, 188. 

CHAPTER XVIIL— Blunders in Word and Blunders 

IN Thought. 

'Purely logical ', 193 — Two kinds of material fallacies, 195. 

CHAPTER XIX.— The Forgotten Issue. 

Petitio principii, 196 — Includes epithets, 197 — And circle, 197 — 
Ignoratio Elenchi, 198 — Includes 'adhominem', 201. 

CHAPTER XX. — The Ill-conceived Universe. 

The assumed universe, 204 — The confusion of universes, 208 — The 
neglected aspect, 211 — The neglected member, 215 — The neglected 
whole, 219. 

CHAPTER XXI. — The Difference between Induction 

AND Deduction. 

; Difference in limitations, 221 — Difference in certainty, 226, 



Vlil CONTENTS. 

CHAPTER XXIL— The Uniformity of Nature. 

How we come to believe in it, 228 — Its two main aspects, 232 — 
Law, 237 — Precision in uniformity, 238 — The thing-aspect of this 
precision, 241— Proof of uniformity, 243. 

CHAPTER XXni. — Science and the Peculiarities of 

THE Relations that it Traces. 

Twofold work of science, 244 — Peculiarities of individual identity 
and causal interaction, 245. 

CHAPTER XXIV.— The Method of Exhaustion and 

THE Search for Particular Uniformities. 

* Perfect induction', 250— Why we accept less, 251 — Justification 
practical, 252 — When may we guess? 252 — How problems and re- 
lations are interwoven, 253. 

CHAPTER XXV. — Induction by Simple Enumeration 
AND THE Search for Causes. 

Analysis, inference, and explanation, 257 — Analysis and clear 
thinking, 259. 

CHAPTER XXVI.— The Methods of Difference and 

Agreement. 

Different ways of exhausting the universe, 261 — The method of dif- 
ference, 262 — The method of agreement, 264— Does either method 
really exhaust ? 265 — Advantages of each, 267 — Plurality of pos- 
sible causes, 267 — Two kinds of data compared, 270 — Post hoc ergo 
propter hoc^ 272— Advantages of experiment, 272— Assumption in 
experiment, 273. 

CHAPTER XXVIL— The Joint Method of Agreement 

AND Difference. 

Its function, 275 — Compared with simple method of difference, 278, 

CHAPTER XXVIIL— Counteracting and Complex 

Causes. 
Counteracting causes, 281— Causes •compounded* or ^combined', 
283, 



CONTENTS. IX 

CHAPTER XXIX. — The Methods of Residues and 
Concomitant Variations. 

Quantitative treatment of causes, 287— Method of residues, 288— 
Method of concomitant variations, 290 — Cautions, 293. 

CHAPTER XXX.— Group Comparisons, or the Method 

OF Statistics. 

Principle and uses, 296 — Number of data, 300— Personal equation, 
etc.. 300— Preconceptions and interests, 302 — Accidental selection, 
304 — Misplaced accuracy, 306. 

CHAPTER XXXL— Means, or Averages. 

General conception, 312— Various kinds, 313 — First use of average, 
317 — Second use of average, 320 — Third use of average, 324 — 
Measures of error, 327. 

CHAPTER XXXn.— Probability. 

Why needed, 330 — What it is not, 331— What it is, 333 — What 
value? 334 — Why hard to estimate, 336— Caution, 337 — Mathe- 
matical principles, 338 — Four more cautions, 340. 

CHAPTER XXXIII.— Observation and Memory. 

Observation and inference, 343 — Credulity, 345 — Errors cumulative, 
347 — Unprejudiced observers, 347 — Two classes of errors, 348— 
Memory and its dangers, 350 — What we remember, 350— Honest 
lies, 352 — Resulting commonplaces, 354. 

CHAPTER XXXIV.— The Discovery of Past and 
Future Events in General. 

The starting-point, 357 — The limit, 358— ' Monuments ', 359— Cir- 
cumstantial evidence, 361. 

CHAPTER XXXV.— Testimony. 

Its importance, 363— Its unique value and danger, 364 — Accepting, 
rejecting, and weighing, 364— Expert evidence ; caution. 367— In- 
ferring without trusting, 371— More refined methods^ 373— Who is 



CONTENTS. 

the witness ? 376 — Joint authorship, 378 — How does he know ? 384 
— Hearsay, 384— Is he truthful? 386 — Arbitrary tests, 386 — 
Character, 387 — Circumstances, 388 — Interests, 389 — Consistency 
and general probability, 392 — Confirmation and contradiction, 
393 — The judge must judge impartially, 397 — According to evi- 
dence, 398 — Must judge for himself, 398 — Must have a problem and 
make it definite, 400 — Issue before evidence, 402 — Must not be 
managed by the witnesses, 403 — Must not decide in a hurry, 404. 

CHAPTER XXXVL— The Three Ultimate Tests of 

Truth. 

Consistency, 405 — Conceivability, 406 — The third test, 409 — Uni- 
formity in the mass, 409 — Analogy, 413 — Absurdity, 414 — Sim- 
plicity, 416 — The right to assume these principles, 421 — The 
limits of proof, 423. 

Exercises 427 

Index 4^5 



LOGIC. 

CHAPTER I. 
INTRODUCTION. 

The business of Logic is to help us to think clearly and 
objectively, express ourselves plainly and accurately, reason 
correctly, and estimate aright the statements and arguments 
of others. 

We cannot fully understand what is meant by the state- 
ment that logic helps us to think clearly unless we dis- 
tinguish carefully between two kinds of thinking. 

The first kind makes some statement or asks Two kinds of 

tninkiiig:. 

some question; the second consists in a mere 
play of mental images, such as takes place when we follow 
quite passively the successive notes of a piece of music, 
hearing each as it passes but doing nothing more, or when 
the music runs through our head afterwards in the same 
way, or when half-dozing we watch the pictures that float 
before us, or when in the same passive way we feel yet do 
not note the sensations that come from our limbs as we 
walk or row or take some other such mechanical exercise. 
But just as soon as we recognize that the music is or is not 
beautiful, that one note is following another, that some one 
is playing, or that we are hearing, feeling, or imagining 
something, then we get back for the moment at least to 
the first kind of thinking; for to the mere passive images 



2 INTRODUCTION. 

we have added something else and there is now an active 
affirmation or denial. 

The second kind of thinking — that which consists in the 
mere play of sensations or images — serves no purpose beyond 
the pleasure or recreation of the thinker; and logic has 
nothing to do with it. Consequently, w^hen w^e speak of 
clear thinking we do not refer to the vividness or continuity 
of such passive images, but rather to the definiteness and 
consistency of active affirmations, denials, or questions. 

When we affirm or deny anything we are said to form a 
belief, to come to a conclusion, or to pass a judgment; and 

the sentence in which the judo^ment is expressed 
Judgments . ^^ , . . V> ,• ^ 

andpropo- is called a proposition. Froposiiions can thus 
sitions. 1 1 r> 1 . . , 

be denned as sentences expressing judgments. 

According to this definition interrogative sentences are not 
propositions, for a question implies the absence of a judg- 
ment. On the other hand negative sentences are proposi- 
tions; for it is quite as much an act of judging to deny that 
something is the case, e.g., to say or think ' The day is not 
hot', as to affirm it — to say or think 'The day is hot'. 
There is thus a vast difference between saying that a thing 
is not so and not saying that it is so, in spite of the fact that 
we often say ' I do not think so ' when we mean ' I think 
not '. 

Judgments always have reference to something other than 
themselves. Like the eye which always looks outward and 
never sees itself, they are always concerned with some object 
or other which lies beyond them, and never with themselves. 
This is most important. Perhaps it can be made clear by 
an illustration from grammar. When I say " The word 
' good ' is an adjective ", I am speaking of that word as it 
occurred somewhere else; for as I use it here it is a noun. 
W^ords never refer to themselves, but to something else 
which they name or ' mean '. The same is true of judg- 
ments. When I say " The house is on fire ", I do not mean 
to state anything about myself or about my judgment with 



JUDGMENTS AND VRDPOSTTIONS. 3 

reference to the house. I do not even mean to say that I 
judge that the house is on fire. I do judge it; and the 
statement expresses my judgment. But to express a judg- 
ment is to tell something about the object thought about or 
judged of — in this case the house — not about the thought 
or judgment itself, or the person who passes it, or the words 
in which it is expressed. When we wish to see our own 
eyes we do not look at them directly, but at their image in a 
mirror. So when we wish to know our own thought we 
must get a new thought with the thought in question as its 
object, e.g,, ' I thought that the house was on fire', or 
* I recognized that the house was on fire '. In these proposi- 
tions I am talking about my own thought or judgment; in 
the former I was not. But even here the thought of which 
I am speaking is not the thought that I am expressing, for 
I am speaking of the past thought and expressing the present 
thought about it. 

That about which a judgment is passed, i.e., that about 
which something is asserted (affirmed or denied), is called 
the Subject or Object of our thought. If it is a real thing or 
person, it is also called the subject of the relations that are 
affirmed of it, and the w^ord used to point it out is usually 
the subject of the sentence or proposition in which the judg- 
ment is expressed. Thus, in the example just given, the 
real house is the subject of the state we call being on fire, 
for it is the house — not something else — that is blazing; the 
real house is the subject of the judgment, for it is the real 
house that I am thinking and speaking about; but it is the 
word ' house ' that is the subject of the sentence. It is not 
the word ' house ' that is on fire or of which I am thinking 
or speaking, and it is not the real house that is part of a 
sentence. Thus the subject of a sentence is not that about 
which something is stated in the sentence, but it is the name 
^that about which something is stated. 

We should never confuse these three different meanings 
of the word Subject — what we are thinking about, or the 



4 INTRODUCTION. 

subject of thought; the thing that is in a certain state, or 
the subject of that state; and the name of what we are 
thinking and speaking about, or the subject of a sentence. 

There are plenty of logicians and other writers who have 
not made or recognized this distinction. Locke, for exam- 
ple, who wrote more than two hundred years 
A different ,, ... . , ■, ^ ^ ^ 

view of ago, tells us m his celebrated Lssay Concernmg 

judgments. ^-t tti t- y> ^ ^ 11 -HI 

Human Understandmg that knowledge is the 

perception of the agreement or disagreement of our ideas '\ 

This definition takes no account whatever of the things 

beyond our ideas to which they are supposed to refer» So 

Jevons tells us in his " Lessons in Logic ", a text-book that 

is very widely used, that an act of judgment " consists in 

comparing together two notions or ideas of objects derived 

from simple apprehension, so as to ascertain whether they 

agree or differ ". But when we judge that the house is on 

fire we do not compare our idea of the house with our idea 

of fire, find that in some way or other the two ideas ' agree ', 

and then use the copula ' is ' to indicate the agreement and 

to fasten the two agreeing ideas together. On the contrary 

we are usually wholly absorbed in the house and its fate and 

do not think about our own ideas at all. When we say that 

a person can tell ' only about his own ideas of things ' it 

would be more accurate to say that he can express only his 

own opinions. But to express an opinion about a thing 

is to tell not about the opinion itself — about one's own 

thoughts and their relations to each other — but about the 

thing as one believes it to be, its states and its relations to 

other things. If we really agreed with Locke when he says 

or implies that everything we know is our own idea instead 

of something beyond it, we should have to agree also w4th 

Hume when he says that we " can form ideas which shall be 

no greater \i,e., larger] than the smallest atom of the animal 

spirits of an insect or a thousand times less than a mite'', 

merely because we can think of things so small; when he 

speaks of perceptions or sensations as " composed of parts " 



A DIFFERENT VIEW OK JUDGMENTS. 5 

because the things that \ve perceive or feel are so composed; 
and when he seriously discusses " the infinite divisibility of 
our ideas of space and time. '' * 

If there is no distinction between thought and the object 
thought of, Flume is right enough in talking of large and 
small ideas; but if there is a distinction, we must not assume 
that a thought of a large or complex object is any larger than 
the thought of one that is small or simple. A good photo- 
graph of a single brick involves just as complex a chemical 
process on the sensitive plate as that of a whole house; to 
pick a single grape is just as complex an act as to pick a 
whole bunch; and in the same way to think of a mob is not 
to have a mob of thoughts. Some acts of thinking are un- 
doubtedly more complex than others; but the complexity 
of the thought in no way corresponds with that of the object 
thought about, f 

* See his <' Treatise of Human Nature", Book I, Part II, Sec. I. 
David Hume lived from 17 ii to 1776. He was probably the greatest of 
all British philosophers. 

+ As for the ' simple apprehension ' spoken of by Jevons and so many 
other writers, it has little or nothing to do with an act of judgment. We 
can divide a sentence into subject and predicate, or, if we like, into 
subject, predicate, and copula ; but we cannot make any such division 
in the judgment which the sentence expresses. " Simple apprehension ", 
says Jevons, " is the act of mind by which we merely become aware of 
something, or have a notion, idea, or impression of it brought into the 
mind. The adjective simple means apart from other things, and appre- 
hefision the taking hold by the mind. Thus the name or term /r<?« in- 
stantaneously makes the mind think of a strong and very useful metal, 
but does not tell us anything about it, or compare it with anything else." 
{^Eleinentary Lessons in Logic ^ p. ii.) But let the reader spend five min- 
utes trying to think of such a metal without making some statement 
about it. He can say ^ Iron is strong,' or ' Iron is useful,' or ' Iron is 
a metal,' or 'This is iron,' and during the five minutes he will doubt- 
less make an immense number of other statements; but when he tries to 
think of it without discovering some relation or passing some judgment 
he will probably find himself mechanically repeating some word appli- 
cable to iron and really thinking about something else; or it may be 
that with the word upon his lips or some visual image in his phantasy 



6 INTRODUCTION. 

Since all thinking has reference to some reality beyond 

itself, we think clearly when we discern the object that we 

are thinking about without confusion, and we 

thinking: is reason correctly when we see how one relation 

objective. r ^ • - ^ 1 T ^ 1 . , 

ot a thing involves another, in order to think 
clearly and reason correctly it is therefore necessary to look 
outwards continually beyond ourselves and beyond the words 
used by others towards the things that we or they are think- 
ing about, in order to see these things and all their essential 
relations as they are. Unless we do this we cannot succeed 
either in expressing ourselves plainly and accurately or in 
forming a right estimate of the reasoning of others. Thus 
the habit of closely examining the reality beyond us and of 
testing all our thoughts and words with reference to that 
reality is necessary for all the aims of logic. 

Logic is often defined as the science of the laws of 
thought; but if what we have been saying is correct, it would 
Scope of be far more appropriate to say that it points out 

logic. ^j^^ i^^^.g ^^ things which all thought should 

respect, or that it deals with the mutual implications of the 
relations of things. The special sciences and metaphysics 
also study relations of things and the way in which one 
involves another, but with a somewhat different purpose. 
Each of the special sciences is concerned with some one 
group of things and relations, and when it inquires how one 
relation involves another it is for the sake of gaining more 
knowledge about the particular things and relations in ques- 
tion. Its aim is thus the attainment of wider or more exact 
knowledge in some one special field. Metaphysics, on the. 
other hand, inquires into the most fundamental and general 
relations of all things, and tries to find out what the inmost 
nature of anv thing must be in order that all of these rela- 
tions should belong to it together. Logic, like metaphysics, 

he will find consciousness itself flickering and disappearing. — If simple 
apprehensions exist, they form no part of our knowledge, of our coherent 
thought, or of our reasoning. All these involve judgments. 



TRUTH IMPERSONAL. 7 

has a very general aim; it too inquires into the most funda- 
mental relations of things and the way in which one in- 
volves another. But its inquiry is not so profound as that 
of metaphysics; it does not ask what the inmost nature of 
things must be in order that these relations should exist 
together in them; and the knowledge that it does try to 
gain about relations and their mutual implications it regards 
as a means, not as an end. We cannot reason at all in sci- 
ence or anything else unless we have some idea of them, and 
we cannot reason correctly unless our idea of them is essen- 
tially correct; but it may be correct enough to enable us to 
reason well about most subjects without being nearly so 
profound as advanced metaphysical inquiries try to make it. 
Thus in so far as logic tries to make us reason correctly by 
giving us correct conceptions of things and the way in w^hich 
their relations involve each other, it is a kind of simple meta- 
physics studied for a practical end. 

There is a sense, however, in which i^ is perfectly true that 
logic deals with ' laws of thought \ A kw of t"bGught tells 
how people actually do think, just as a law of astronomy 
tells how heavenly bodies actually move, and the real science 
of the laws of thought is therefore psychology; but inasmuch 
as there are certain natural ways of thinking that lead to 
various kinds of logical blunders, it is necessary to understand 
them in order to understand why we make the blunders. 
Thus in so far as logic deals with various kinds of fallacies 
which we naturally commit and tries to explain their origin, 
it is touching on the field of psychology and dealing with 
' laws of thought '. 

Every judgment, true or false, asserts something about 
some supposed reality beyond itself, and the difference 
between the true and the false is that the state of Truth im- 
affairs asserted by the former really exists and P^^^®^^^* 
that asserted by the latter does not. Whether it does or 
does not depends altogether upon the nature of things and 
the presence or absence of the conditions that might naturally 



8 INTRODUCTION. 

produce it. It does not depend at all upon the judgment 
about it. Whether the sun is shining or not at a certain 
place depends altogether upon the time of day and the pres- 
ence or absence of clouds, fog, and an eclipse. If such 
conditions as these are all favorable, the sun is certainly 
shining whether I happen to think so or not; and if I say it 
is not shining when it really is, my statement is false no 
matter who I am or how sincere I may be in making it; so 
likewise if I have nervous prostration or a broken leg, I have 
it no matter who says that I have or that I have not. 
Hence it is arrant nonsense to say that something may be 
* true for one person and false for another'. One person 
may believe that a statement is true and another may believe 
that it is not, but the facts are what they are wholly regard- 
less of these conflicting beliefs, and one of the persons must 
be wrong. If every possible statement could really be true 
for one person and false for another, then every one would 
always be right in what he thought no matter what it was, 
and there would be no such thing as an error or mistake, 
and therefore no distinction between correct thinking and in- 
correct. All logic is based on the assumption that there is 
such a distinction, and therefore from the standpoint of logic 
no blunder could be more fundamental or destructive than 
that which is involved in the serious belief that something 
may be ' true for one person and false for another \ 

The notion that some fact might exist 'for' one person 
and not ' for ' another doubtless arises from the existence of 
individual differences in matters of taste and a certain con- 
fusion about their meaning. If a picture pleases me, I say 
it is beautiful ; and if it displeases you, you say it is ugly; and 
all that either of us has any right to mean by the statement 
is that the picture does please him or displease him. Each 
statement thus tells about the relation between two things, 
the picture and the beholder; and because of the difference 
between the two beholders both statements understood in 
this way may be perfectly true; the picture really is beautiful 



COROLLARY. 9 

for me and really is ugly for you, and there is nothing more 
to be said — de gustibus nil disputandum. But these words 
* beautiful ' and ' ugly ' and others like them have the same 
grammatical form as words like ' square ' and ' round ' 
which really tell about the thing itself, quite regardless of its 
relations to the beholder; and this helps to make us ignore 
the difference betw^een them and assume that somehow or 
other we can describe the thing itself (as we do with such 
words as ' round ' and ' square '), wdiile at the same time the 
truth of the description depends (as it does w^ith such words 
as ' beautiful ' and ' ugly ') upon who it is that gives it. 

Somewhat like the statement that something may be true 
for one person and false for another is the statement that it 
may be true in one science and false in another. Towards 
the end of the middle ages the monkish philosophers found 
themselves reaching conclusions that w^ere quite contrary to 
the doctrine of the Church wdiich they were bound to accept. 
So they said that tliere was a difference between theology 
and philosophy, that a doctrine might be true in one though 
false in the other, and that they accepted all the teachings 
of the Church as true in theology, though they might reject 
a part of them as false in philosophy. By this subterfuge 
they tried to give an excuse for continuing their thinking as 
freely as possible and yet save their heads by remaining in 
nominal subservience to the Church. Of course this doctrine 
of a ' double truth ' was nothing but a subterfuge, and it dis- 
appeared when men gained the righc to exercise their own 
individual judgment in matters of belief. 

Since the reality with which all thought is concerned is 

something different from the thought itself, we have no right 

to assume without evidence that there is anv 

1-1 1 1 111 1 • " Corollary. 

relation between them beyond the bare relation 

of knower and object known. We have no right to assume 

that our thoughts are like things — e.g,, that our thought of 

the moon is round like the moon itself — or that they have 

the same history or are subject to the same laws. We have 



I a INTRODUCTION. 

no right to assume, for example, that distant events are any 
more vague than those of the present simply because our 
ideas of them are more vague, or that things were vague and 
chaotic before they were definite because our ideas of them 
were. 

Facts are as independent of our feelings as they are of our 
ideas. Hence when we are trying to find out what the facts 
Fact and really are we must not ask instead what we 
feeling. should like them to be and assume that we have 

answered the first question when we have only answered the 
second. Yet obvious as this is, the tendency to confuse the 
facts as they are with what we should like them to be is 
exceedingly strong. Indeed it is so strong that hardly any 
one can overcome it altogether. To do so — to look facts 
squarely in the face and accept them as they are, no matter 
how pleasant or unpleasant they may be — is one of the very 
first conditions of greatness, and it is always a mighty aid to 
success in any career. Moreover it is something which does 
not require any unusual mental ability. But it does require 
intellectual honesty; and because very few of us are willing 
to be absolutely honest in our thought those who are so 
often seem heroic. The ' Appeal to Consequences \ on the 
other hand — the argument which really invites one to accept 
a certain view merely because the view itself or something 
else that it involves is more pleasant to believe in than the 
contrary — is thoroughly contemptible, and yet it is some- 
thing to which we are so accustomed that it takes a strong 
man with a great love for truth to show us how contemptible 
it really is. I quote the following from the account of the 
discussion of evolution at the Oxford meeting of the British 
Association in i860 in the Life of Professor Huxley 
(vol. i. pp. 197-8): " The Bishop spoke thus ' for full half 
an hour with inimitable spirit, emptiness, and unfairness. ' 
* In a light, scoffing tone, florid and fluent, he assured us 
there was nothing in the idea of evolution ; rock-pigeons were 
what rock-pigeons had always been.' '' Then " he rhetori- 



FACT AND FEELING. II 

cally invoked the aid of feeling, and said, ^ If any one were 
willing to trace his descent through an ape as his grand- 
father, would he be willing to trace his descent similarly on 
the side of his grandmother P' '' "On this Mr. Huxley 
slowly and deliberately arose. A slight tall figure, stern and 
pale, very quiet and very grave, he stood before us and spoke 
those tremendous words — words which no one seems sure 
of now, nor, I think, could remember just after they were 
spoken, for their meaning took away our breath, though it 
left us in no doubt as to what it was. He was not ashamed 
to have a monkey for his ancestor; but he would be ashamed 
to be connected with a man who used great gifts to obscure 
the truth. No one doubted his meaning, and the effect was 
tremendous. One lady fainted and had to be carried out; 
I, for one, jumped out of my seat.'' 

No one can think clearly and reason correctly or be relied 
upon by others as fair-minded and impartial who believes that 
any view of things is right if it is not true, or who does not 
strive with all his might to see things as they really are in 
spite of all his wishes. 

Our feelings tend to influence our judgment not only by 
making us believe what it is pleasant to believe, but also by 
making us believe whatever happens to fit in with the 
emotion of the moment. Leslie Stephen says: ' We are not 
unhappy because we believe in hell; but we believe in hell 
because we are unhappy. ' When we are despondent the 
world seems dark and sad, when we are happy it seems 
bright and glad, when we are in love it is easy to find 
*' Helen's beauty in a brow of Egypt", and when we are 
angry or irritated it is hard to believe that anger or irritation 
is out of place. 

'* Speak roughly to your little boy, 
And beat him when he sneezes. 
He only does it to annoy, 

Becauses he knows it teases." 

This certainly is the logic of the emotions, and it is hard 



1 2 INTRODUCTION. 

enough to overcome it — until the mood is over; and if we 
must wait until then to see things as they are, we should also 
make it a rule to wait before we express or act upon our 
judgments. Hence the wisdom of counting one hundred 
before displaying anger, and of the regulation which obtains, 
I believe, in the British navy requiring that no officer shall 
punish a man until twenty-four hours after the supposed 
offence. 

In our effort to see things as they are in spite of our 
wishes and emotions we .often have to resist an appeal to 
them made wittingly or unwittingly by some one else. 
When any one discusses the qaestion at issue on its own 
intrinsic merits he is said to reason io the point, or, as the old 
logicians would say, his is an Argumentiwi ad Rem; but when 
one party to a discussion takes advantage of the weakness of 
another and tries to persuade him that something is true by 
appealing to his wishes or his emotions he uses one form of 
the Argumentum ad Hominem. Since the essential purpose 
of this so-called argument is to leave a person in a certain 
mood which will affect' his judgment, it makes very little 
difference how it is done. It may be by gentle or inflamma- 
tory speeches or it may be without speech at all — by feeding 
him or embarrassing him or getting him out in the moon- 
light. 

The Argumentum ad Populum is essentially the same as this 
form of the Argumentum ad Hominem except that it is 
addressed to a crowd. The real arguments of successful 
political speakers are generally very weak. They carry. their 
point and get the votes merely by gaining the sympathy of 
the audience: by getting it to feel in harmony with the 
speaker and out of harmony with his opponents; and it does 
not make much difference whether this is done by solid 
arguments, impassioned appeals, ridicule and abuse of the 
other side, or funny stories, 



CHAPTER II. 

THE MEANINGS OF WORDS. 

I In almost all our thought and our communication with 

others we use words. A word is " a mark which may raise 

in our mind a thought like to some thought which we had 

before, and which, being pronounced to others, may be to 

them a sign of what thought the speaker had before in his 

mind". Unfortunately, however, the thing or the relation 

which a given word is used to mark is not always the san:ie. 

and if we assume that it is in any particular case when in 

fact it is not, we are bound to misunderstand each other, to 

make some egregious blunder in our own reasoning, or not 

to notice such blunders in the reasoning of others. 

To speak first of the blunders of interpretation. These 

often arise when a student is beginning the study of any 

science and takes it for granted that words which 

, . Ill 1 • Blunders of 

are used m a purely technical sense are used m interpreta- 

the popular sense to which he happens to be 
accustomed. The word ' phenomenon ' as used in science 
merely means something that we perceive or appear to per- 
ceive, but the student assumes that it means something 
strange or miraculous. When the psychologist speaks of 
' imagining ' something he merely means forming a mental 
picture of it; but the student may assume that he means 
believing something that is not so. ' Immediate ' in science 
means direct or without the assistance of anything else; but 
the student will probably assume that it means without any 

13 



14 THE MEANINGS OF WORDS. 

delay. A ' particular ' proposition in logic is one that tells 
about some undesignated part (cf. 'particle') of a class; 
but the student who reads his book in a hurry assumes that 
it is one that tells about some individual in particular. 
When a student misinterprets statements in this way he is 
almost certain to misconceive the meaning of the whole 
paragraph or chapter in which they occur, or to gain no 
definite idea from it whatever. This may be partly the fault 
of the author, for if a book is intended as an elementary 
text-book, it is his business not to use words in these new 
senses without saying something about it. But it is also 
largely the fault of the student himself. He knows that the 
author is trying to convey some definite meaning; and if he 
took the trouble to inquire what that meaning really is, 
instead of being satisfied with his work when he has read the 
words or learned to jumble some of them together, he would 
see very easily that some of these words must be used in a 
strange sense. 

The same trouble occurs also very frequently in history 
and literature. If a book was written more than a century 
ago, many of its words will have been used in a sense with 
which we are no longer familiar; and here again unless we 
are very careful we are likely to misunderstand the author's 
meaning completely. What, for example, is the m_eaning 
of the italicised words in the following passages from the 
Bible ? *' I may /e/l all my bones: they look and stare upon 
me " (Ps. 22:17). "I prevented the dawning of the morning, 
and cried: I hoped in thy word'' (Ps. 119:147). "But 
unto thee have I cried, O Lord; and in the morning shall 
my prayer prevent thee " (Ps. 88: 13). " That I may show 
all thy praises within the ports of the daughter of Sion " 
(Ps. 9:14, Prayer-book version). " My daughter is grievously 
vexed y^\i\i a devil '' (Matt. 15: 22). What also is meant by 
the word * let ', by the word * meat ' in the phrase ' meat 
and drink', by * rod ' and 'staff' in Ps. 23, and by the 
phrase ' What have I to do with thee t ' What did the 



BLUNDERS OF INTERPRETATION. 15 

Biblical writers mean by a ' prophet ' , by ' cherubim ', and 
by a ' penny ' as the word is used in the story of the Prodigal 
Son ? What is meant in Magna Charta when it says, '' No 
free man shall be taken or imprisoned . . . but by lawful 
judgment of his peers " P * 

If words do not mean anything when they are taken in a 
sense with which we are familiar, we can be sure that the 
author was either writing nonsense or using them in some 
sense with which we are not familiar. But even when they 
do mean something when taken in our ordinary sense, that 
may not be what the author meant them to mean. Hence 
students of historical methods say that we must not read 
some old writings for the purpose " of extracting information 
from it without any thought of first ascertaining exactly what 
was in the author's mind ". If we do, we are sure to give 
the author's words our meaning instead of his. Therefore 
we must make it a rule to understand the exact meaning of 
what is said " before asking what can be extracted from it 
for the purpose of history '',f or for any other purpose. 
The Bible, for example, is full of the deepest truths; but 
most of us read it without finding them simply because the 
rhythm is pleasant and the words are familiar and it never 
occurs to us to inquire whether or not the men who wrote 
them meant to say anything that we have not thought already, 
and if they did, what it is. 

This finding of the meaning, even where it seems plain 
enough already, is no mere perfunctory matter. To be sure 



* A student of philosophy should pay particular attention to the mean- 
ing of such words as 'Idea', 'Perception', 'Impression', 'Reflection', 
as used by Locke, by Berkeley, and by Hume; the phrase ' Moral Philos- 
ophy ' as used by Hume and his contemporaries ; ' Conceive ' as used in 
different contexts by Herbert Spencer ; ' Substanz ', ' Wirklichkeit ', 
' Realitat ', ' Noumenon ', and ' Ding an sich ' as used by Kant, and the 
like. 

fLanglois-Seignobos, '^ Introduction to the Study of History", pp. 
143-146 (Henry Holt S^ Co., 1898). 



1 6 THE MEANINGS OF WORDS. 

that we have done it aright we should have studied the 
language of the time and country as well as of the author 
himself. But the essence of the method is always the same 
— to find a meaning or a set of meanings for a word which 
will enable us to give a reasonable interpretation to every 
passage in which it occurs.* 

But we need not go to science and literature to find words 
misunderstood. Such misunderstandings occur continually 
in every-day life, and often do great mischief. 

There are various ways in which words may become 

ambifruons, or 2:et several meaninofs that are liable 
How words T X J T • , 

become am- to be contused. Jevons gives three ot them as 
Mguous. , ,, 

lollows: 

1. From the accidental confusion of different words; e.g., 
the adjective 7neaii may signify medium or average (from the 
French jnoyen), ox despicable (from the Anglo-Saxon ^^;;^(:^;?^); 
light may signify the opposite of heavy (from the same root 
as levis^ or the opposite of dark (from the same root as lux). 

2. From the transfer of meaning from the original objects 
to others associated with them; e.g., the words house, court, 
church, all mean either a place or those that meet there. 

3. From the transfer of meaning to analogous objects. 
The word sweet is applied to sounds and innumerable other 
things that give pleasant feelings, though none of these feel- 
ings is similar in any other respect to sweet tastes. Similarly- 
l\i^ foot of a mountain, the ha7td of a clock and th^^leg of a 
table do not bear any close resemblance to human limbs, 
but in certain respects they answer the same purpose. As 
Whately puts it, " leg : animal :: supporting stick : table " . 
It is by the same kind of analogy that recent writers speak 
of society as an organism. 

* " ' These studies of words ', said Fustel de Coulanges, 'have a great 
importance in historical science. A badly interpreted term may be a 
source of serious error.' And, in fact, simply by a methodical applica- 
tion of interpretative criticism to a hundred v^ords or so, he succeeded in 
revolutionizing the study of the Merovingian epoch." (Op. cit., p. 150.) 



BLUNDERS OF INTERPRETATION. 17 

The more difference there is between a word's different 
meanings the more likely we are to discover the ambiguity 
before it has done much harm. When any one whatam- 
speaks of ' the church ' we are not likely to con- are mo^s\^ 
fuse a building with the group of people that ^^^^^^°^^* 
worships in it. The context soon shows which he means. 
But we very well might confuse different larger and smaller 
groups of worshippers. When we are told that such and 
such is the custom or practice of ' the Church ' it might be 
hard to tell whether the speaker was referring to the com- 
municants or voting members of a certain particular congre- 
gation, to the congregation as a whole, to the denomination, 
to a particular group of denominations, excluding Roman 
Catholics, Unitarians, or others that the speaker regarded as 
heretical, to the Western Church in all its branches, or to 
the whole body of those who call themselves Christians. 
Even when we are sure which of these bodies he means we 
may still be unable to say what proportion of the individuals 
in the body he intends to include when he says that such is 
the piactice of ' the Church '. One person might say that 
something was the practice of ' the Church ' if it were done 
habitually by a third of the individual members; another 
might not say so unless it were done by two-thirds or three- 
quarters; and still a' third might deny that anything was the 
practice of ' the Church ' even if it were done habitually by 
all the members so long as it was not done officially by the 
body as an organized whole under the direction of the proper 
officers. 

Words which are ambiguous because we cannot tell how 
much or how little they are intended to include are called 
Vague. The word Church in the last example was vague 
because it did not show precisely what individuals the speaker 
intended to include in the group that he used it to indicate. 
In other cases the ambiguity is about relations: a word is 
used to indicate a group of them, but we cannot tell precisely 
what they are. This vagueness is characteristic of many of 



1 8 THE MEANINGS OF WORDS. 

our commonest words, and is explained by the way in which 
we begin to use them. 

*'' In Geometry ... we learn the definitions of the words 
used, point, line, parallel, etc., before we proceed to use 
them. But in common speech, we learn words first in their 
application to individual cases. Nobody ever defined good 
to us, or fair, or kind, or highly educated. We hear the 
words applied to individual objects; we utter them in the 
same connection; we extend them to other objects that strike 
us as like without knowing the precise points of likeness that 
the convention of common speech includes. The more 
exact meaning we learn by induction from individual cases. 
Ugly, beautiful, good, bad — we learn the words first as appli- 
cable to things and persons: gradually there arises a more or 
less definite sense of what the objects so designated have 
in common. Tiie individual's extension of the name 
proceeds upon what in the object has most impressed him 
when he caught the word; this may differ in different in- 
dividuals; the usage of neighbors corrects individual eccen- 
tricities.'' 

The more complex and intangible the object or relation 
which a word is used to indicate the greater is the danger of 
misunderstanding from its ambiguities. '' Take such words 
as monarchy, tyranny, civil freedom, freedom of contract, 
landlord, gentleman, prig, culture, education, temperance, gen- 
erosity, . . . Let two men begin to discuss any proposition 
in which any such word is involved, and it will often be 
found that they take the word in different senses. If the 
relation expressed is complex, they have different sides or 
lines of it in their minds; if the meaning is an obscure 
quality, they are guided in their application of it by different 
outward signs. 

" Monarchy, in its original meaning, is applied to a form 
of government in which the will of one man is supreme, to 
make laws or break them, to appoint or dismiss officers of 
State and justice, to determine peace or war, without control 



BLUNDERS OF liNTERPRETATlON. IQ 

of Statute or custom. But supreme power is never thus 
uncontrolled in reality; and the word has been extended to 
cover governments in which the power of the titular head is 
controlled in many different modes and degrees. The exist- 
ence of a head, with the title of King or Emperor, is the 
simplest and most salient fact; and wherever this exists the 
popular concept of a monarchy is realized. The President 
of the United States has more real power than the Sovereign 
of Great Britain; but the one government is called a 
Republic and the other is called a Monarchy. People dis- 
cuss the advantages and disadvantages of monarchy with- 
out first deciding whether they take the word in its etymo- 
logical sense of unlimited power, or its popular sense 
of titular kingship, or its logical sense of power definitely 
limited in certain ways. And often, in debate, monarchy 
is really a singular term for the government of Great 
Britain. 

''Culture^ religions, ge?terous, are names for inward states 
or qualities: with most individuals some simple outward sign 
directs the application of the word — -it may be manner, or 
bearing, or routine observances, or even nothing more sig- 
nificant than the cut of the clothes or of the hair. Small 
things undoubtedly are significant, and we must judge by 
small things when we have nothing else to go by; but instead 
of trying to get definite conceptions for our moral epithets, 
and suspending judgment till we know that the use of the 
epithet is justified, the trifling superficial sign becomes for 
us practically the whole meaning of the word. We feel that 
we must have a judgment of some sort at once : only simple 
signs are suited to our impatience. 

" It was with reference to this state of things that Hegel 
formulated his paradox that the true abstract thinker is the 
plain man who laughs at philosophy as what he calls abstract 
and unpractical. He holds decided opinions for or against 
this or the other abstraction, freedom, tyranny, revolution, 
reform, socialism, but what these words mean and within 



^C THE MEANINGS OF WORDS. 

what limits the things signified are desirable or undesirable 
he is in too great a hurry to pause and consider." "^ 

Here is an example of some of the mischief done by 
ambiguous words in economics: "The discussion of 'the 
relations of labor and capital ' has not hitherto been very 
fruitful. It has been confused by ambiguous definitions, 
and it has been based upon assumptions. . . . 

" Let us first examine the terms. 

" (i) Labor means properly toil, irksome exertion, expen- 
diture of productive energy. 

" (2) The term is used, secondly, by a figure of speech, 
and in a collective sense, to designate the body of persons 
who, having neither capital nor land, come into the produc- 
tive organization offering productive services in exchange 
for means of subsistence. These persons are united by 
community of interest into a group, or class, or interest, 
and when interests come to be adjusted, the interests of 
this group will undoubtedly be limited by those of other 
groups. 

" (3) The term labor is used, thirdly, in a more restricted, 
very popular and current, but very ill-defined way, to desig- 
nate a limited sub-group among those who live by contribut- 
ing productive efforts to the work of society. Every one is 
a laborer who is not a person of leisure. Public men, or 
other workers, if any, who labor but receive no pay, might 
be excluded from the category, and we should immediately 
pass, by such a restriction, from a broad and philosophical 
to a technical definition of the labor class. But merchants, 
bankers, professional men, and all whose labor is, to an 
important degree, mental as well as manual, are excluded 
from this third use of the term labor. The result is, that 
the word is used, in a sense at once loosely popular and 
strictly technical, to designate a group of laborers who 
separate their interests from those of other laborers. Whether 
farmers are included under ' labor ' in this sense or not I 

* Minto's Logic, pp. 83-87 (Scribners, 1893). 



BLUNDERS OF INTERPRETATION. 2t 

have not been able to determine. It seems that they are or 
are not, as the iaterests of the disputants may require. . . . 

'* (i) Capital is any product of labor which is used to 
assist production. 

" (2) This term also is used, by a figure of speech, and in 
a collective sense, for the persons who possess capital, and 
who come into the industrial organization to get their living 
by using capital for profit. To do this they need to 
exchange capital for productive services. These persons con- 
stitute an interest, group, or class, although they are not 
united by any such community of interest as laborers, and, 
in the adjustment of interests, the interest of the owners of 
capital must be limited by the interests of other groups. 

*' (3) Capital, however, is also used in a vague and pop- 
ular sense which it is hard to define. In general it is used, 
in this sense, to mean employers of laborers, but it seems to 
be restricted to those who are employers on a large scale. 
It does not seem to include those who employ only domestic 
servants. Those also are excluded who own capital and 
lend it, but do not directly employ people to use it. 

" It is evident that if we take for discussion ' capital and 
labor', if each of the terms has three definitions, and if one 
definition of each is loose and doubtful, we have everything 
prepared for a discussion which shall be interminable and 
fruitless, which shall offer every attraction to undisciplined 
thinkers, and repel everybody else. ' ' * 

Here is another example from the same source: *' There 
is no possible definition of ' a poor man '. A pauper is a 
person who cannot earn his living; whose productive powers 
have fallen positively below his consumption; who cannot, 
therefore, pay his way. . . . But he is not the ' poor man \ 
The ' poor man ' is an elastic term, under which any number 
of social fallacies may be hidden. Neither is there any 
possible definition of ' the weak '. Some are weak in one 

•^Sumner, -'What Social Classes Owe to Each Other," pp. 81-84. 
(New York: Harper & Bros.) 



^2 THE MEANINGS OF WORDS. 

way, and some in another; and those who are weak in one 
sense are strong in another. . . . 

" Under the names of the poor and the weak, the negli- 
gent, shiftless, inefficient, silly, and imprudent are fastened 
upon the industrious and prudent as a responsibility and a 
duty. On the one side, the terms are extended to cover the 
idle, intemperate, and vicious, who, by the combination, 
gain credit which they do not deserve, and which they could 
not get if they stood alone. On the other hand, the terms 
are extended to include wage-receivers of the humblest rank, 
who are degraded by the combination. The reader who 
desires to guard himself against fallacies should always 
scrutinize the terms ' poor ' and ' weak ' as used, so as to 
see which or how many of these classes they are made to 
cover. ' ' "^ 

When two persons use words in different senses it is not 
surprising that one should reject a statement which the other 
accepts. What is surprising is that we fail so often to 
discover that our difference is not about the external facts 
at all, but only about the meaning of the words. Often a 
discussion does end in our looking up words in a dictionary. 
But it ought not to end there; for if we fully realized the 
difference between the words that we happened to use and 
the things and relations that we used them to indicate, we 
should come back from the dictionary and ask what was the 
real point of difference between us with reference to these 
things and relations. For surely it was these and not the 
meaning of words that we meant to discuss. 

Vague and ambiguous words not only make us misunder- 
stand others. They do worse, and make us misunderstand 
Blunders of ourselves and commit bad blunders in conse- 
mference. quence. Since a word is a mark intended " to 
raise in our mind a thought like to some thought which 
we had before'', we naturally take it for granted that any 
thought which the word does raise in our mind is the one 
* Sumner, 1. c, pp. 20, 21. 



BLUNDERS OF INFERENCE. 23 

which we had before when we used it; and if we have con- 
cluded that a statement is true we suppose it to be true abso- 
lutely, without its ever occurring to us that it might be per- 
fectly true when the words are taken in one sense and 
utterly false when they are taken in another. But if words 
are ambiguous and we take them in one sense when we are 
inquiring into their truth and then take them in a different 
sense when we are asking what can be inferred from their 
truth, it is evident that we may easily reach some conclusion 
which w^e never would have reached if the two different 
thoughts had not happened to be expressed or suggested 
by the same word. Sometimes these plays on words are so 
obvious that they are only intended to amuse a hearer. 
Sometimes they are intended to puzzle him; it is perfectly 
evident that the conclusion does not follow; but the words 
make it seem as though it should; and the puzzle is to 
explain why. Often, however, the words really do deceive 
both speaker and hearer. As Bacon says: " Men imagine 
that their minds have the command of language; but it often 
happens that language bears rule over their minds.'' Here 
are some examples of various kinds. 

We know that we ought to control our tempers, and we 
happen to have expressed this by the statement that it ^ is 
wrong to be irritated ', and to remember the words. A phy- 
sician finds that a patient who needs absolute quiet is being 
constantly disturbed by various noises, and in stating the 
fact he happens to say in his technical language that the 
patient is constantly ^ irritated '. This is the word used in 
the formula that we happen to remember: it is wrong to be 
irritated ; and so, without stopping to ask what the physician 
means by it, we jump to the conclusion that the patient is 
constantly doing something wrong. 

* Lincoln says you cannot fool all the people all the time ; 
but Mr. G. at his bargain-sales fools all the people and he 
fools them every time ; therefore Lincoln was wrong. ' 
Here the trouble lies in the ambiguity of the phrase ' all the 



24 THE MEANINGS OF WORDS. 

people ' and in the assumption that ^ all the time ' means the 
same as ^ every time ' . ' All the people ' in the second sentence 
means all the people at the bargain-sale ; but Lincoln meant 
by it all the people in the country. ^ Every time ^ as it is used 
here means every time Mr. G. has a bargain-sale; but * all 
the time ' as Lincoln used the phrase means for a long con- 
tinuous period in the life of a nation. 

' A saving man is a blessing to the community ; a miser is 
a saving man ; therefore a miser is a blessing to the com- 
munity.' Here the word ' saving' may be ambiguous or it 
may not. If we understand by ^ a saving man ' in the first 
sentence any one whatever who saves his money instead of 
spending it, then the conclusion follows from the facts 
assumed. But it is more likely that any one who grants the 
truth of the first statement is thinking of ^ a saving man ' as 
one who exercises reasonable economy in contrast to a spend- 
thrift. If this is so, we make him say more than he intended 
if we extend the meaning of the word ^ saving * so as to include 
those who exercise unreasonable economy ; and thus the 
argument is unfair. 

* A teacher must know how to teach ; Mr. R. , who has 
just taken up the work, does not know how to teach ; there- 
fore Mr. R. cannot be a teacher.' Here there are several 
ambiguities. * A teacher ' may mean any one who earns his 
living in a schoolroom, or it may mean a ^ true * or ideal 
teacher. When we say he must know how to teach we may 
mean that if he does not he is not a teacher (as when we say 
a square must have four sides); we may mean that he ought 
to know ; or we may mean that if any one does not know he 
will not be allowed to attempt the work. ' Know how to 
teach ' is ambiguous in two respects. In the first place, to 
^ know how ' may mean to understand the principles involved, 
it may mean to have a certain amount of practical skill 
whether one understands the principles or not, and it may 
mean to have both principles and skill. In the second place 
the phrase ^ know how ' is vague because it does not tell us 



BLUNDERS OF INFERENCE. ^5 

how much knowledge the speaker has in mind. When he 
says that a teacher must ' know how ' to teach, does he mean 
that he must be able to do it according to the latest approved 
principle, or does he merely mean that he must be able to do 
it as well as any intelligent person could ? Even ^ teach ' 
is ambiguous. Does it mean merely to give instruction in 
certain subjects, or does it mean also to keep order in the 
schoolroom and instil good morals and manners ? The phrase 
* cannot be ' in the conclusion of the argument has much the 
same ambiguities as * must ' in the first part of it. Does it 
mean * certainly is not ', 'will not be permitted to be', or 
' cannot become ' ? If the premises mean that an ideal 
teacher has a certain amount of knowledge or skill and that 
Mr. R. has not, the conclusion follows that Mr. R. is not an 
ideal teacher ; but it does not follow that Mr. R. is not 
earning his living in a schoolroom, that he is excluded from 
the teaching profession, or that he cannot become an ideal 
teacher ; and so with the other meanings of the various 
sentences. 

The following curious arguments are taken from a book 
written to prove that a lie is never justifiable, and have 
doubtless imposed upon a large number of readers as well as 
the author himself.* 

A) *^ Truth is, so to speak, the very substratum of Deity. . . . 
As there is no God but the true God, so without truth there 
is and can be no God." 

B) '^ As Christ is Truth, those who are in Christ must never 
violate the truth. . . . This would seem to be explicit enough 
to shut out the possibility of a justifiable lie." 

C) ''We cannot conceive of God as God, unless we con- 
ceive of him as the true God, and the God of truth. If there 
is any falsity in him, he is not the true God. Truth is of God's 
very nature. To admit in our thought that a lie is of God, is 

* Trumbull, <'A Lie Never Justifiable", pp. 135, 145-6, 223. 224. 
The first extract is given as a quotation from Hodge's '^ Systematic The- 
ology ", and the second as a summary of Martensen. 



26 THE MEANINGS OF WORDS, 

to admit that falsity is in him, or, in other words, that he is 
a false God." 

D) ** A lie is the opposite of truth, and a being who will 
lie stands opposed to God, who by his very nature cannot lie. 
Hence he who lies takes a stand, by that very act, in opposition 
to God. Therefore if it be necessary at any time to lie, it is 
necessary to desert God and be in hostility to him so long 
as the necessity for lying continues." 

Let us examine these arguments. In A the author sup- 
poses his reader to take for granted that ' There is no God 
but the true God '. From this it is supposed to follow that 
' Without truth there is and can be no God ' ; from this that 
'Truth is, so to speak, the very substratum of Deity'; and 
from this that a lie is never justifiable under any circum- 
stances. But what do these words all mean? When he 
expects every one to admit that ' there is no God but the true 
God \ he must mean by it that there is no God but the god 
that really exists, whatever we may call him, and whatever 
his nature may be. If the next step follows from this, * With- 
out truth there is and can be no God ', these words must be 
taken to mean that if there is no reality — if there is nothing 
real — there is and can be no real God. This same thought 
is expressed in the next set of words : 'Truth' — that is to 
say, reality — ' is the very substratum of Deity '. But from 
this fact that God would not exist if nothing real existed it 
surely does not follow that a lie is never justifiable. The 
only reason that it seems to follow is that the word ' truth ' 
is ambiguous, and when the author says that ' truth ' is 
the very substratum of Deity he forgets that when this was 
proved it meant that reality was the substratum of Deity, and 
now he takes it to mean that always making true statements 
and disapproving of every false statement is ' the very sub- 
stratum of Deity'; and from this it follows that a lie is never 
justifiable. Hence we have to take the words in one sense 
in order that they should follow from what every one is sup- 
posed to admit, and take them in quite another sense in order 



BLUNDERS OF INFERENCE, 27 

that the conclusion should follow from them. So long as we 
think only of the words it is possible to be deceived by the 
argument. When we ask their precise meaning and look 
carefully at the things about which they are supposed to tell it 
is not. 

In B what is meant by the statement that Christ is ' Truth ' ? 
It certainly does not mean that he is an accurate statement. 
Hence this must be taken more or less metaphorically to 
mean that in his life there is to be found a revelation of the 
deepest spiritual truths, that he is a true or genuine mani- 
festation of God, or something of that sort. Christ then 
revealing the true spiritual life, it follows that ^ those who are 
in Christ must never violate the truth', that is, it follows 
that those who are in communion with him should not do 
anything inconsistent with that highest spiritual life. But 
why does this ' shut out the possibility of a justifiable lie ' 
unless we assume what was to be proved, that a lie never is 
justifiable, or in accordance with the highest spiritual life? 
Here again it is only the ambiguity of the word ' truth ' that 
makes the conclusion seem to follow. Unless the statement 
that those who are in Christ must never violate the truth 
means what I have said, it does not follow from what was 
said about Christ -, and unless the sense is then twisted and 
the statement is taken to mean that they must never tell a lie 
under any circumstances whatever, the conclusion does not 
follow from it. 

In C there is the same play on the words ^ true ' and 
' truth ' as in A, and a similar play on the words ^ false' and 
' falsity ' . This becomes very apparent if we omit these 
ambiguous words altogether and substitute for them the 
synonyms that seem to express the meaning most accurately 
in each individual case. The passage wall then read some- 
thing like this : ' We cannot conceive of God as God unless 
we conceive of him as the real God, and the God 0/ reality 
(ox who is trustworthy, or who never approves of a lie). If 
there is any unreality (or untrusiworthiness') in him, he is not 



2 8 THE MEANINGS OF WORDS. 

the real (or trustworthy) God. Reality (or trustworthiness) 
is of God's very nature. To admit in our thought that a lie 
is of {i.e., approved under any circumstances by) God, is to 
admit that unreality is in him, or, in other words, that he is 
a fictitious God.' So long as we do not make any attempt to 
interpret the words the conclusion may seem to be proved ; 
but when we drop the words and consider only the relations 
that they ought to be used to point out it is perfectly evident 
that it is not. 

In D the ambiguity lies in the word ' opposed ' and its 
derivatives. When we say that ' a lie is the opposite of 
truth ' we mean that a false statement is unlike a true one 
and can be contrasted with it just as large can be contrasted 
with small ; and if God ' by his very nature cannot lie ', then 
a being who can and will lie ' stands opposed to God ' in the 
sense that the two can be contrasted, just as a large man can 
be contrasted with a small one. It does not follow in the 
slightest that there is any * hostility ' between them. The 
only reason that the conclusion appears to follow is that the 
words ' opposite ' , ' opposed ^ and ' opposition ' are all de- 
rived from the same root, and we therefore assume when they 
are being used that they all have essentially the same mean- 
ing without stopping to ask what that meaning is until the 
verbal manipulation is over. Then we are told that ' in op- 
position ' means ^in hostility ', and we cannot deny it. As 
a piece of reasoning this sort of verbal jugglery is almost on 
a plane with that which proves something, I have forgotten 
what, by saying that a beehive is a bee-holder, a beholder a 
spectator, and a specked 'tater a bad vegetable. 

This last example shows the danger of so-called Parony- 

mous terms. When a word is not ambiguous in itself we may 

introduce an ambiguity by substituting for it some other word 

derived from the same root and so constructed that 
ParonymoTis 

terms. it seems to point to exactly the same relations, 

when it does not. We have a perfect right to say, ' Romeo is 
in love; lovers are impetuous; therefore Romeo is im- 



HOW TO DEAL WITH AMBIGUITIES. 29 

petuous'; because the words Mn love' and Mover' point to 
precisely the same state of mind. But we have no right to 
say, ^ Schemers are not to be trusted ; this man has a scheme ; 
therefore he is not to be trusted ' ; for one is not a ' schemer ' 
unless his ^ schemes ' are rather dishonest, and are so habit- 
ually. So likewise a man who is once drunken or who once 
lies is not necessarily a drunkard or a liar. Words like these, 
which appear to correspond in meaning but really do not, 
are quite common, e.g,: art, artful; design, designing, 
/aith, faithful ; presume, presumption ; king, kingly ; probable, 
probability ; child, childish. 

When we are confronted with arguments which turn upon 
some ambiguous word wx do not usually see what the trouble 

is all at once ; but we often do have a vague 

. How to 
feeling that there is something wrong; and this deal with 

^ rr ■ i i i i amtoigfuitics. 

ought to be surncient to make us go back and 

examine all the words on which the argument seems to 
turn. The surest way to test the argument is to put it into 
new words altogether, taking care that each one of them 
shall indicate something perfectly definite. Since all correct 
inference is based upon the nature and relations of the 
things in question, and not upon the relations of the 
words in which we happen to speak of them, this method 
of getting rid of the questionable words is perfectly legiti- 
mate and reasonable. When this has been done and we 
realize exactly what the relations in question are, we may 
then go back to the old words and show how they seemed to 
indicate first one and then another. If we wish to avoid 
making such blunders ourselves, we should pursue much the 
same method, and make sure that our argument depends 
upon the relations of things themselves and not upon the 
accidents of language by seeing whether it will seem to hold 
no matter what language we use to denote these relations. 

When words are vague or otherwise ambiguous, it is usu- 
ally wise for the person who uses them in a given connection 
to announce the exact meaning which he intends them Xq 



30 THE MEANINGS OF WORDS. 

express. When he does this he is said to define them. A 

Definition, therefore, is a statement of the meaning of a word 

as used in a given connection, or a statement 
Definition. 

that tells what quahties or other relations an 

object must have in order that the word defined should be 
properly applied to it. By the aid of definitions the same 
word can be used in different senses in different connections 
without confusion. 

When a word of doubtful meaning has not been defined by 
the user the only course for the hearer or reader is to define 
it for himself by comparing the various passages in which it 
occurs. He must try to find some definite meaning which 
will fit them all. This is what the makers of every dictionary 
have to do. By a definite meaning I mean of course a 
definite relation that the word is used to denote, not merely 
a definite set of phrases to put after it in a definition whether 
they mean anything or not. W^e have not found the meaning 
for the word ' toves ' merely because we have learned to say, 
" They are something like badgers — they are something like 
lizards — and they are something like corkscrews". If a 
word has several distinct meanings, or if the meaning is vague, 
the effort to find one definite meaning which will fit the con- 
text in every case will soon make this plain. 

To find a definite meaning for every word and every state- 
ment in the books that one studies is no easy task, and when 
any one first undertakes to do it he will probably be disap- 
pointed to find how little ground he can cover. But unless a 
person seeks one he cannot understand the book thoroughly, 
and unless he does it often enough to feel confidence in his own 
work he cannot tell the difference between a book that means 
something and one that does not. He will not be able to 
^ understand ' the latter, or get definite thoughts out of it, 
but he will not be able to tell whether it is because of his own 
stupidity or because there are no definite thoughts there to 
get ; and if he has not this ability to discriminate, he is likely 
to be the victim of any incoherent writer whose words are 



HOW TO FRAME DEFINITIONS. 31 

sufficiently high-sounding. This ability to interpret what 
one reads or hears and discriminate between sense and non- 
sense is one of the most essential aims of all education, and 
a person who has not taken the trouble to acquire it ought 
not to call himself educated. 

When w^e have found the meaning of a word and come to 
state it two things are essential: to be precise and to be simple. 

To be precise is to tell exactly what the word means 

^ , , -^ , , . . How to 

— no more and no less; to state the characteristics frame 

of an object, in virtue of which the name is appli- 
cable, with perfect definiteness. We must not define a net 
as something made out of string with holes in it, or as some- 
thing to catch fish with. For a net is not necessarily made 
out of string or used to catch fish, and things might be made 
of string and have holes in them, or be used to catch fish, 
without being nets. In the same way we should not define 
man as the animal that laughs, for though man may be the 
only animal that laughs, it is not laughter that makes him man 
and entitles him to the name. He would remain man if he 
never laughed again. So, we should not define virtue as the 
only thing which makes one truly and permanently happy, 
or acid as that which turns blue litmus paper red ; for virtue 
might still be virtue if it ceased to make us happy, and the 
word acid would be quite as applicable to various substances 
if litmus paper had never existed. 

To be simple in a definition is to frame it in such a way 
that it will immediately mean something to the people for 
whom it is intended. Dr. Johnson defines a net as something 
reticulated and decussated, with interstices between the inter- 
sections ; and Herbert Spencer defines evolution as ^^an inte- 
gration of matter and concomitant dissipation of motion, 
during which the matter passes from an indefinite, inco- 
herent homogeneity to a definite, coherent heterogeneity, and 
during which the retained motion undergoes a parallel trans- 
formation." These definitions are precise and to the expert 
they may be pimple, but to ordinary people they are not. 



32 THE MEANINGS OF WORDS. 

Simplicity and precision are difficult to unite, but with 
patience the union can nearly always be made. 

There is an old rule that definitions should be by genus 
2C^^ differ entice. This means that it is not necessary or desir- 
able to enumerate every single attribute of the things denoted 
by the name defined. It is sufficient to tell what class they 
belong to and how they differ from other members of that 
class. If we are defining the word ' bloodhound ' we should 
say that bloodhounds are a certain specified kind of dog. It 
is not necessary to say that they are living things, belonging 
to the animal kingdom, and possessed of a backbone, mouth, 
eyes, ears, teeth, and paws. These attributes and a hundred 
others are all implied by the generic term ' dog '. 

To define a term by itself or by some other equally obscure 
word from the same root, e.g.^ 'a preacher is one who 
preaches \ is practically the same as not to define it at all. It 
adds neither precision nor simplicity. But if two words 
from the same root do not indicate precisely the same rela- 
tions it may be proper to define one by means of the other 
and some modifying phrase, e.g., ^a preacher is one who 
preaches by profession ' , ^ a liar is one who tells lies habit- 
ually \ Again, we are likely to lose rather than gain in both 
precision and simplicity when we define in metaphorical 
language, as when we say that words are barbed arrows, the 
soul is life's star, truth is the food of the soul, or the camel is 
the ship of the desert. The metaphors may bie useful, but 
not as definitions. 

Definitions are usually supplemented by examples, diagrams, 
or other illustrations. These do not make the definition any 

more accurate, for they ove only one case out of 
Illustrations. ^ ^ „'.,./ ^ , / 

many that fall within it, and unless some explana- 
tion is added, they do not show exactly where the dividing 
line is. But they do make the definition easier to understand, 
because they turn one's attention in the right direction. 
When we know some of the things which a boundary is 
intended to include we are better prepared to learn precisely 



ILLUSTRATIONS. 33 

where that boundary is. Because examples give this kind of 
preparation it is often wise to put some of them before the 
formal definition. 

The illustration chosen should be typical. If we try to 
prepare for the definition of virtue by an example, we should 
choose some act or character that is recognized as virtuous by 
everybody ; something well within the class, and, if possible, 
something of which virtue is the most striking feature. To 
prepare for the definition of a fish we should not draw an eel. 
It looks too much like a snake. After the definition is given, 
however, and its general purport is understood it is often wise 
to give an example of something that falls within it and of 
something else quite like it that falls without, and then explain 
why it is that the one is included and the other not. When 
one is making a contrast of this sort one might well use an 
eel to illustrate the difference between a fish and a snake, or 
a whale to illustrate the difference between a fish and a 
mammal. The nearer we get to the boundary on any side 
the easier it is to understand a description of that particular 
part of it. 

When an example is not so striking as to be unmistakable 
we should take pains to make clear in precisely what respect 
it illustrates. It will not do to say, ' The subject of a 
sentence is the name of the thing spoken about, e.g., John 
struck James '. We should underline the word ' John ', put 
it in quotation-marks, or indicate in some other way that it is 
that word that is the subject, and not the real John or the 
word ^ James'. Similarly we cannot explain what a house 
is by merely handing some one a picture and leaving him to 
wonder whether the house is the thing in the background 
with windows or the thing in the foreground with ears. 

The reason why the common uneducated person does not 
recognize the importance of understanding the meaning of 
words precisely is that it is really not very important for his 
purposes. To play out of doors, to find one's way along the 
street and notice what people are doing there, to buy clothes 



34 THE MEANINGS OF WORDS. 

or groceries : all these are very concrete performances, and 

any one can carry them on or tell about them 
Where 
precision is afterwards fairly well without a painstaking choice 

of words. With the work of school and the 
first year or two of college the need for a careful examination 
and selection of words becomes more apparent ; and yet 
only a fair amount of care and skill in the use of words is 
required to tell about the concrete facts of history and 
geography, describe the processes involved in a chemical 
experiment, and even translate concrete statements from a 
foreign language, without confusion. But when we come 
to the abstract sciences, and have to deal, not with the 
surface of things, but with their deeper relations, the case 
is very different. The political economist must make 
sharp distinctions between wealth, capital, and money; the 
psychologist, between sensation and perception, concep- 
tion and imagination, illusion, delusion, and hallucination ; 
the student of ethics, between intention and motive, pleasure 
and satisfaction ; the theologian, between wrong and sin, 
providence and predestination, substance and personality ; 
the lawyer, between torts and crimes, corporations and part- 
nerships, and so on. Here the things under discussion are 
not visible and tangible, and we cannot explain what we are 
talking about by merely pointing the finger. It takes much 
skill to talk or think about them without confusion, and the 
only way to be sure of doing so is to make absolutely clear- 
cut, precise, and rigid definitions, and keep them in mind 
throughout the whole discussion. Such definitions are not 
conventional ornaments at the head of a page, they are 
necessities. 

Although the meaning of every word, and therefore all 
definition, has reference to things, we do not define things. 

Names are defined when we tell Avhat they mean ; 

classes may be said to be ' defined ' when we point 
out their boundaries ; things may be described in sentences but 
never defined, for no words can make them any more definite 



CAUTION. 35 

than they are. The question sometimes raised whether we 
define names or things depends, as Mill has shown, upon the 
fact that some definitions carry with them the assumption of 
the thing's existence in the real word (^e.g., any definition 
of cow or horse), while others do not (e.g., a definition of 
a dragon or of a perfect man). But in each case it is the 
meaning of the word, not the thing, with which the definition 
is primarily concerned. To be sure in the former case we 
can prove a definition to be wrong by showing that it does 
not agree with the thing ; but that is because the name stands 
for the thing, and if the definition does not agree with the 
thing it cannot correctly explain the name. 

In the following chapters it will be necessary to define a 
considerable number of logical terms. The definitions given 
were made with care, but doubtless some of them are incor- 
rect. Every reader is urged to make out as well as he can 
from the explanations, the illustrations, and the definitions 
themselves exactly what each one of them was intended to 
express, and then go back and see whether it really did ex- 
press it or not, and if not why not. This will help him to 
understand the book and — what is far more important — it 
will give him good general practice in the accurate interpre- 
tation and use of words. To increase the opportunities for 
this practice there are among the exercises at the back of the 
book a large number of definitions of these same logical 
terms which are incorrect, and the reader is advised to go 
over as many of them as possible and state clearly and ex- 
actly what is wrong with each. This he will find much 
harder than to merely score them out and put correct ones in 
their places ; but the practice is correspondingly better. 



CHAPTER III. 
THE MEANING OF STATEMENTS AS A WHOLE. 

When we know the literal meaning of every individual 
word and phrase used by a speaker or writer there is still 
danger of misinterpreting him ; for often people do not in- 
tend what they say to be taken seriously and literally. 

Not seriously, for he may be using some customary phrase 

which is hardly intended to mean anything at all. If a 

letter begins with the phrase ' Dear Sir ' and ends with 

^. * Yours faithfully ^ or ' Your obedient, humble 
Conventional -^ ' 

phrases. servant', or even if the words are somewhat 

more effusive, we must not conclude that the writer neces- 
sarily meant any more than to be polite. He may be writing 
to his worst enemy. And of course there are correspondirig 
forms and phrases in every age and country. When a 
Spaniard tells you that his house is yours he does not 
expect you to ask for the title-deeds. Even official documents 
are not free from such polite phrases. The Grand Remon- 
strance was really an indictment containing over two hundred 
counts against the King himself, drawn up in 1641 when 
the Parliament and King were on the verge of civil war, 
and yet the petition with which it was presented begins as 
follows: "Most Gracious Sovereign, Your Majesty's most 
humble and faithful subjects the Commons in this present 
Parliament assembled, do with much thankfulness and joy 
acknowledge the great mercy and favor of God in giving 
your majesty a safe and peaceable return out of Scotland into 

36 



OBLIQUE SENSES. 37 

the Kingdom of England, where the pressing dangers and 
distempers of the State have caused us with much earnestness 
to desire the comfort of your royal presence y and Hkewise the 
unity and justice of your royal authority ' ' , etc. 

In the United States such terms as ' liberty ' and ^ home ' 
have been used so much for all sorts of political purposes that 
they have ceased to have any very definite meaning when 
they are used in political and social controversies. The other 
day, for example, I read in a newspaper editorial that the 
Boers in the present war (1900) were fighting for ' their 
liberty and their homes '. Of course this is only a rhetorical 
way of saying that they are fighting for a certain form of 
political independence, but a reader who had no other sources 
of information might very well conclude from it that the 
British government really wanted to take forcible possession 
of private property and drag the owners off into slavery. 

When a person expects something that he says to be 
taken seriously, he may still not expect to have it taken lit- 
erally. ^^It is possible that he may have used Qijuq^e 
some expressions in an oblique sense ; there are senses, 
several kinds of cases where this occurs : allegory and sym- 
bolism, jests and hoaxes, allusion and implication, even the 
ordinary figures of speech, metaphor, hyperbole, litotes. In 
all these cases it is necessary to pierce through the literal 
meaning to the real meaning, which the author has purposely 
disguised under an inexact form." * The devil quoted scrip- 
ture accurately enough, but took it altogether too literally 
when he set Jesus on the pinnacle of the temple and said to 
him, " If thou art the Son of God cast thyself down : for it 
is written. He shall give his angels charge concerning thee : 
and on their hands they shall bear thee up, lest haply thou 
dash thy foot against a stone ' ' . 

Many other examples of these oblique senses are to be 

* Langlois-Seignobos, p. 151. Hoaxes might have been omitted. 
They can hardl}^ be said to contain a ' real meaning disguised under an 
inexact form ', 



3 8 THE MEANING OF STATEMENTS AS A WHOLE. 

found in the Bible. The Beast and the Scarlet Woman in 
the Apocalypse and the visions in the second part of Daniel 
are certainly not intended to be taken literally. And the 
books of Job and Jonah ? Shall they be taken in the direct 
sense as history or in the oblique sense as allegory ? Surely 
we must ask what a document really means before we can ask 
whether it is true or demand that any one accept the truth 
which it contains. 

'' A parallel difficulty occurs in the interpretation of illus- 
trative monuments ; the representations are not always to be 
taken literally. In the Behistun monument Darius tramples 
the vanquished chiefs under foot : this is a metaphor. Me- 
diaeval miniatures show us persons lying in bed with crowns 
on their heads : this is to symbolize their royal rank ; the 
painter did not mean that they wore their crowns to sleep 

Exaggeration as a form of oblique speech demands special 
consideration. It is so common with some people that they 
constantly assume that what they say will be discounted, and 
Exaffffer- ^^ ^^^ realize all that is meant by the statements 
ation. of others unless they are likewise exaggerated. A 

picture that pleases them is the most beautiful they ever saw, 
a pleasant evening is the best time they ever had in their 
lives, and so on. A person who says what he means, no 
more and no less, may very well be deceived into attaching 
altogether too much importance to the statements of such 
people ; and they, on the contrary, are likely to attach alto- 
gether too little to his. If he says that some men are honest, 
they assume that he means to say that most are not ; if he 
gives qualified praise they assume that he does not mean 
to praise at all or that he means to damn with faint praise. 

* Langlois-Seignobos. — "Only one general principle [for detection 
of oblique meanings] can be laid down, and that is, that when the 
literal sense is absurd, incoherent, or obscure, or in contradiction with 
the ideas of the author or the facts known to him, then we ought to 
presume an obliq^ue sense." (Op. cit., p. 152.) 



AMPHIBOLOGY. 39 

Hence there is always danger of misunderstandings when 
persons accustomed to accurate statements are interpreting 
those who are not, and vice versa. 

Exaggeration, however, is not only a matter of personal 
habit. Under the name hyperbole it is recognized as a cor- 
rect form of literary expression; and not to make allowance 
for it is to misinterpret the passage in which it occurs, e.g, : 
*^If a man can number the dust of the earth, then shall thy 
seed also be numbered " ; ' ^ He was owner of a piece of ground 
not larger than a Lacedemonian letter"; " He was so gaunt, 
the case of a flageolet was a mansion for him ". 

In connection with this interpretation of statements as a 
whole, it is customary for writers on logic to point out several 
kinds of blunders, to which they have given characteristic 
names, as follows. 

To commit the ' Fallacy of Amphibology ' is to misinterpret 
a sentence because its construction is ambiguous. The tradi- 
tional examples are from ambiguous oracular deliv- 
erances, e.g.^ ' Aio te ^acida Romanos vincere 
posse ' (I say that you ^acus the Romans are able to con- 
quer); ^The Duke yet lives that Henry shall depose '. Ex- 
quisite care was needed to make such ambiguous construc- 
tions as these, but most of those we meet are the result of gross 
carelessness, e.g,\ ' Wanted — a piano, by a young lady made 
of mahogany '; ' He finished his business and returned on 
Wednesday ' ; ' Twice two and three '; ' He who necessarily 
goes or stays (z'.^. , who necessarily goes or who necessarily 
stays) is not a free agent, you must necessarily go or stay 
{i.e., take the alternative), therefore you are not a free 
agent '.* The confusion can always be remedied by a recon- 
struction of the sentence ; often by a mere change in punc- 
tuation or in the position of a word. 

The name ^ Fallacy of Accident ' is applied to three differ- 
ent kinds of blunders : 

i) When a statement about the mere substance of some 
* Whately gives this last as a fallacy of composition. 



4Ct THE MEANING OF STATEMENTS AS A WHOLE. 

individual thing is interpreted as referring to its condition 
(accident) as well, e.g., ' What you bought yester- 
day you eat to-day; raw meat is what you bought 

yesterday; therefore you eat raw meat to-day'. 

2) When an abstract statemiCnt about some of the relations 
or essential characteristics of a certain kind of thing is in- 
terpreted as a concrete statement about every thing of the 
kind in all its relations (accidents), * e.g., ' Meat is good for 
food, this spoiled horse-flesh is meat, therefore this spoiled 
horse-flesh is good for food '; ^ I do not admire tall women, 
A. B. is a tall woman, therefore I do not admire A. B.'. In 
these examples the major premises really refer to ' Meat as 
such ' or ' the essential characteristics of meat ', ' tall women 
as such ' or * tallness in women '. 

3) When any loose statement really intended to tell only 
what is true ' under ordinary conditions ' or ' other things 
being equal ' or ' usually ' (though such phrases are omitted) 
is interpreted as though it meant to tell what is true always, 
no matter how unusual the conditions, e.g., * Strychnine is a 
deadly poison, therefore this minute dose is sure to poison me '; 
* The use of medicine is to be avoided (when possible), there- 
fore this sick man must not touch it ' ; ' Corporal punishment 
is debasing (as a rule), therefore this bully should not be 
thrashed '. 

In all of these examples the Fallacy of Accident has been 
Direct ; the reasoning has been from a statement concerning 
the substance, essence or rule, without reference to any acci- 
dent or special condition, to a case in which such accident is 
present {a dido simpliciier ad dictum secundum quid). But 
corresponding to each of the three kinds of direct fallacy 
there is also the Converse Fallacy of Accident (a dicto secun- 
dum quid ad dictum simpliciter) where the accident or special 
condition is implied in the major premise and omitted in the 

* In the first case the accident is contrasted with Aristotle's ' mate- 
rial ' or Locke's ' real ' essence ; in the latter with Aristotle's '■ formal ' 
or Locke's 'nominal' essence. 



ACCIDENT. 41 

minor and conclusion, e.g.\ (i) ^ What you liked yesterday 
you like to-day, you liked this (fresh) bread yesterday, there- 
fore you like this same (stale) bread to-day'; (2) 'I admire 
A.B. and CD.; A.B. and CD. are tall women ; therefore I 
admire tall women' (as such); (3) ' Strychnine is a magnificent 
remedy (for certain diseases and in certain doses), A.B. needs 
a remedy, therefore he should take strychnine '.* 

Direct or converse fallacies of accident of the first class are 
comparatively rare and trivial. Those in the two other 
classes (which are not always easily distinguished from each 
other) can be avoided by insisting upon accurate statements or 
explanations if the speaker is present and willing to make them; 
but when authoritative interpreters are not at hand they may 
cause interminable discussions and disputes. Everybody 
admits, for example, that lying is wrong ; but does that mean 
that every act that involves a lie is wrong, or only that lies 
as such are wrong, and acts that involve a lie are wrong pro- 
vided that there is no other and more important moral considera- 
tion involved? If we interpret the law in the first sense it is 
wrong to lie to a madman or a murderer to save the life of a 
child ; if in the second it is right, provided that the obliga- 
tion to save an innocent life is greater than the obligation to 
always refrain from lying, and that to tell a lie is the only 
available way of saving it. Human relations are so complex 
that we can only discuss one aspect of them at a time ; and 
it may very well be that some moral laws at least have reference 
not to acts as a whole but to aspects of them, and that in in- 
terpreting such laws one aspect must be balanced against 
another and the one indissoluble concrete act judged by the 
most important moral consideration involved. 

The interpretation of moral law^s is a question of ethics, but 

* The article ' a ' lends itself easily to this kind of confusion. ' I ad- 
mire a tall woman ' may mean that I admire some individual woman 
who happens to be tall or that I admire tallness in women. It is this 
confusion that gives point to the time-honored conundrum, 'What 
makes more noise than a pig under a gate ? ' ' Two pigs.* 



42 THE MEANING OF STATEMENTS AS A WHOLE. 

if we accept a law in one sense and then apply it in the other 
we commit the logical fallacy of accident. 

The fallacy of ' Accent ' is essentially a fallacy of interpre- 
tation. It consists in misinterpreting an author (i) by un- 
duly accenting some particular word in a sentence, 
e.g. , ' Thou shalt not bear false witness against thy 
neighbor', or ^ Thou shalt not bear false witness against thy 
neighbor' ; * or (2) by taking passages out of their immediate 
context, e.g. , proving that Dr. Watts believed in dog-fights be- 
cause he said '^ Let dogs delight to bark and bite ", or proving 
future punishment by John xv. 6 : '' And men gather them 
and cast them into the fire and they are burned", or by 
Matt. xxii. 13 : '^ Cast him into outer darkness ; there shall be 
weeping and gnashing of teeth" ; or (3) by appealing to 
some particular passage, even a long one, though it may be 
contrary to the whole spirit of the author quoted. This is a 
form of the fallacy of which the members of any Christian 
sect might very well accuse the members of all the others. 
The controversy as to the whole spirit of the gospels which 
such an accusation would raise would be much more profit- 
able than any amount of quibbling over a few proof texts. 

A remarkably clear exposition of this fallacy is given in 
the preface to Matthew Arnold's ^' Literature and Dogma", 
from which I quote a few sentences. It is of course his 
account of the fallacy in which we are interested, not his 
views on the Bible. 

'^The homo unius libri, the man of no range in his reading, 
must almost inevitably misunderstand the Bible, cannot treat 
it largely enough, must be inclined to treat it all alike, and 
to press every word. . . . He has not enough experience of 
the way in which men have thought and spoken, to feel what 

* Jevons quotes the passage from the Book of Kings, ' And he spake 
to his sons, saying, Saddle me the ass. And they saddled him \ But 
this is surely a case of amphibology. The accent on the word <■ him * 
changes the meaning of the passage only because it changes the ante- 
cedent to which the pronoun refers. 



ACCENT. 43 

the Bible-writers are about; to read between the lines, to 
discern where he ought to rest with his whole weight, and 
where he ought to pass lightly. . . . And thus we come back 
to our old remedy of culture, — knowing the best that has been 
thought and known in the world ; which turns out to be in 
another shape, and in particular relation to the Bible : getting 
the power J through reading, to estimate the proportion and rela- 
tion in what we read. If we read but a very little, we nat- 
urally want to press it all ; if we read a great deal, we are 
willing not to press the whole of what we read, and we learn 
what ought to be pressed and what not. Now this is really 
the very foundation of any sane criticism. . . . Things are on 
such a scale, and progress is so gradual, and what one man 
can do is so bounded, that the moment we press the whole of 
what any writer says, we fall into error. He touches a great 
deal : the thing to know is where he is all himself and his 
best self, where he shows his power, where he goes to the 
heart of the matter, where he gives us what no other man 
gives us or gives us so w^ell. ' ' 

The danger of this fallacy of accent is well recognized by 
jurists, and by their rules of evidence they try to guard 
against it. * ^ ^ I have always ' , said Lord Tenterden, ' acted 
most strictly on the rule, that what is in writing shall only 
be proved by the writing itself. My experience has taught 
me the extreme danger of relying on the recollection of 
witnesses, however honest, as to the contents of written in- 
struments ; they may be so easily mistaken that I think the 
purposes of justice require the strict enforcement of the 
rule' ". This is one reason. But then Tenterden goes on 
to say : *^ *By applying the rule to such cases the Court ac- 
quires a knowledge of the whole contents of the instrument, 
which may have a different effect from the statement of a 
part.'''* 

So with confessions and other statements against the inter- 
est of the person who makes them. The law gives them 
* Greenleaf, ''Law of Evidence ", Vol. I, Sec. ^Z. 



44 THE MEANING OF STATEMENTS AS A WHOLE. 

great weight, but it also insists that they shall not be garbled. 
'' In the proof of confessions, as in the case of admissions in 
civil cases, the whole of what the person said on the subject 
at the time of making the confession should be taken to- 
gether. ... It is not reasonable to assume that the entire 
proposition, with all its limitations, was contained in one 
sentence. . . . Unless the whole is received and considered, 
the true meaning and import of the part which is good evi- 
dence against him cannot be ascertained. ' ' * 

On the same principle it is a rule of evidence that if a 
witness tells about a part of any conversation the lawyer who 
cross-examines him has a right to ask about any other part of 
the same conversation. 

The difference between the fallacy of Accent and the fal- 
lacy of Accident in the broader sense of each is this : the 
former misinterprets a writer by confusing incidental state- 
ments with essential ; the latter confuses aspects of things or 
situations (or statements about such aspects) with the things 
or situations (or statements about them) as a whole, f 

* Greenleaf, op. cit., Sec. 218. 

-(■ Whether we should call the over-emphasizing of some one aspect of 
the moral code accent or accident would thus depend upon whether 
we regarded the law as a revelation each part of which should be inter- 
preted with reference to the whole, or as an analysis of conduct into 
various good and bad aspects, several of which may be combined in the 
complex whole. An aspect of a law taken for the whole law is ac- 
cent ; an aspect of an act taken for the whole act is accident. 



CHAPTER IV. 

DIVISION AND CLASSIFICATION. 

To avoid confusion in the use of names we must define 
them; but all definition of names involves a classification of 
objects. If the words ^ animal ', ^ red ', Werte- Relation to 
brate ' have any definite meaning at all there definition, 
must be some things to which they can be properly applied 
and some things to which they cannot, and the things to 
which any one of them can be applied must all have the 
qualities or relations which the name implies, and therefore 
resemble each other in this respect, while the things to 
which it cannot be properly applied must all resemble each 
other in not having these qualities or relations. Hence every 
time we use a name we imply the existence of two classes of 
things : those that have the quality or relation which the 
name implies and those that have not. To define a name 
is to distinguish between these two classes, and the more 
clearly we understand this difference between the things the 
more clearly we can define the word. Hence we shall stop 
speaking about words for a little and speak about the prin- 
ciples of Division or Classification. At the end of the 
chapter we shall return to the discussion of words and their 
interpretation. 

When we have made two classes to one or other of which 
every object in the world can be assigned ac- principles 
cording as it has or has not some given quality or ?^^^^^^^°^ 
relation, each of these classes can be subdivided suMivision. 
with reference to some other quality or relation; and this 

45 



46 DIVISION AND CLASSIFICATION. 

process can be carried on indefinitely, as in the following 
table. 

Substances 

I 



Corporeal = Bodies Incorporeal 

I 

Living = Organisms Inanimate 

_J 

1 I 

Capable of feeling = Animals Incapable of feeling = Plants 



I I 

Rational = Man Irrational = Lower Animals 



_ I I 

Etc. Etc. 



This division and subdivision of everything into precisely 
two. classes according to the presence or absence of some 
given mark (technically called Division iy Dichotomy^ is 
often useful, and in the example just given seems very ap- 
propriate, but there are cases in which it is cumbersome and 
rather absurd, e.g. : 

Colored Objects 

1 



I I 

Red Not Red 



Orange 



Not 

1 


Orange 




1 1 

How Not Yellow 

1 


1 
Green 




1 
Not Green 
1 



Etc- Etc. 

In this case it would be better for almost every practical 
purpose to divide directly into Red, Orange, Yellow, Green, 
and the other colors. Hence instead of dividing according 



CROSS-DIVISION. 47 

to the presence or absence of some given quality [e.g. , red- 
ness), we may divide according to the determination in some 
given respect {e.g., color), making as many co-ordinate classes 
as there are different determinations in that respect; and 
then we can proceed to subdivision, with reference to other 
respects, if such subdivision is necessary, immediately and 
without so much confusion. 

Colored Objects 

r \ I \ I 

Red Orange Yellow Green, etc. • 

I I 



I I I I 

Light Dark Light Dark 

Whether each class should or should not be subdivided in 
the same respect as every other {e.g., each color into light 
and dark), depends altogether upon the purpose of the divi- 
sion. Often it is impossible. Creatures with a nervous 
system, for example, could be divided according to its 
arrangement or development. Those without one could 
not. 

The one great rule for division is that each of the objects 
divided shall have one place in the system, and only one. Thus, 
if we should divide all human beings into Americans, Europe- 
ans, and uncivilized peoples, we should commit a double 
blunder, for some peoples, such as the Japanese, would not 
fall under any head, and some of the American Indians would 
fall under two. 

When any object falls into each of two co-ordinate classes — 
as in this example — there is said to be a Cross-division, 
This is always likely to occur whe?i zve classify objects in 
more than one respect at a time. If we had first d-oss- 
divided peoples according to their geographical division. 
distribution and afterwards subdivided each group according 
to their civilization, or vice versa, this could not have 
occurred, e.g,^ 



48 



DIVISION AND CLASSIFICATION. 



I. American ^ 



II. European 



III. Asiatic 



IV. African 



V. Australian 



VI. 



Other 
islanders 



A. Civilized 



B. Uncivilized < 



A. Civilized 

B. Uncivilized 

A. Civilized 

B. Uncivilized 

A. Civilized 

B. Uncivilized 

A. Civilized 

B. Uncivilized 

A. Civiliz ed 

B. Uncivilized 



1. Savage 

2. Barbarous 



Id. 



To be sure, the uncivilized Indians still fall into two 
classes, Americans and uncivilized Americans, but this is 
now perfectly proper, because the classes are no longer 
co-ordinate ; the latter is subordinate to the former. 

Cross-division is a particularly bad logical blunder, because 
of the mental confusion which is shown by the indiscriminate 
use of several principles of classification (technically called 
Fundamenta Divisionis) at once. 

^^Overlapping, however, may be unavoidable in practice, 
owing to the nature of the objects. There may be objects 
in which the dividing characters are not distinctly marked, 
objects that possess the differentiae of more than one group 
in a greater or less degree. Things are not always marked 
off from one another by hard and fast lines. They shade 
into each other by imperceptible gradations. A clear separa- 
tion of them may be impossible. In that case you may 
allow a certain indeterminate margin between your classes, 
and sometimes it may be necessary to put an object into more 
than one class." * 

* Minto's *' Logic/' p. 95. 



CROSS-DIVISION. 



49 



Cross-division should be distinguished from cross-refer- 
ences, such as one finds in the subject-catalogues of libraries. 
If one does not know whether to put a book on the history of 
English philosophy under ^ History ' or ' England ' or 
' Philosophy ' , he can solve the question practically by 
putting it under one of them, say 'England', and then 
saying under each of the other heads ' See also England '•. 

The blunder of dividing in such a way as to leave out alto- 
gether some object that ought to have been included is likely 
to be the result of haste rather than of confusion. Where one 
knows all the objects that are to be divided, he must look 
about carefully to see that none are omitted. Where he does 
not he must leave room in his scheme of division and subdi- 
vision for additions, e.g. : 



II. Semitic 

III. Turanean 

IV. Others? 



I. Indo-European < 



A. Slavonic 



Russian 
Others ? 



B. Graeco-Roman 

C. Celtic 



D. Teutonic 



E. Others? 



f I. English 

I 2. German 

3. Dutch 

4. Others? 



It need hardly be added that a surbordinate class should 
not contain any objects not included in the class above it. 
If we are classifying serious w^orks of history it would not do 
to include Dumas' ''Three Musketeers " in one of the subdi- 
visions, even though it contains some historical matter, for it 
is not a serious work of history. 

Students should make themselves familiar with the follow- 
ing names : Genus is the name of a class of objects divided 
into smaller classes. Each of these smaller classes is called a 
Species, Where there is a system of divisions and subdivisions 



so DIVISION AND CLASSIFICATION. 

any class is called a species with reference to those above 

it, a ^enus with reference to those below it, e,^.. 
Some ' o 7 o 7 

technical organisms or living bodies are a ' species ' of 
bodies, but are a ' genus ' of which animals are 
a species. In such a system the highest class of all is called 
the Summum Genus ; the lowest, the Infima Species, ' ' When 
a thing is so peculiar and unlike other things that it cannot 
easily be brought into one class with them, it is said to be 
sui generis, or of its own genus";* ^-g-y the rings around 
Saturn amongst heavenly bodies, the ornithorhyncus and 
amphioxus amongst animals. The qualities peculiar to the 
members of some one species or genus, and in virtue of which 
that species or genus is distinguished from other species or 
genera, are called the Differentice of the species or genus. 
Thus the possession of reason, by which men may be dis- 
tinguished from the lower animals, can be called the differ- 
entia of the human species. Qualities peculiar to a species, 
but not used in defining it or distinguishing it from other 
species, are called Properties, or Propria. Thus laughter is 
a proprium of human beings. Qualities or states not char- 
acteristic of a species are QdiA^^ Accidents. 

So far we have taken up the purely formal or negative 
aspect of division, and pointed out the blunders which any 
system of division should avoid. But every 
ciasSf^a^- a-ctual system of division has a purpose, and to 
tion and its attain a purpose it is necessary to move in some 
definite direction, not merely to avoid the pitfalls 
on the road. A scientific classification is nothing more than 
a system of division carried out in such a way as to best serve 
a given purpose. 

One purpose served by classification is to enable a person 
to find any given object with the least possible trouble. If I 
have only two or three dozen books it is not worth while to 
arrange them on the shelf in any particular order, for I can 

* Jevoiis, 



SCIENTIFIC CLASSIFICATION AND ITS PURPOSES. 51 

always find the one I want at a single glance. But if I have 
a library full of books and pamphlets, and I want to be sure 
of finding one of them at a moment's notice, I must arrange 
them alphabetically, or topically, or in some other fixed 
order. When the things themselves cannot be arranged 
according to any plan, the next best thing is to arrange their 
names in some fixed order — usually alphabetical — and after 
the name write where the thing is to be found. In this way 
we construct directories and gazetteers and the indexes of 
books. 

A second purpose served by classification is to give an 
easy means of identifying an object when it is found. A 
suspicious looking person is arrested by the police and they 
wonder who he is ; so they turn up their classified list of 
criminals, looking up (say) the class ' Eyes, blue ' ; then the 
subdivision ^ Height, five feet eleven inches ' ; then the 
further subdivision ^Fingers, tapering '; and so on, till at 
last they find the photograph or thumb-mark of the individual 
in question with his name and record. If the descriptions 
were not classified the work of identifying the man might be 
endless. 

A function similar to these two, yet distinguishable from 
them, is to enable us to find or identify a given kiyid of object. 
Often we do not know what book or man we want to find, 
but the classified list can tell us. We want some book or 
other about colonial furniture, and the subject-catalogue 
names several ; we want a man who can mend china, and 
the classified list of tradesmen at the end of the city directory 
gives a number of names and addresses. In the same way if 
we find a new kind of plant in the woods and want to know 
what it is, we use some botanical ' key,' in which kinds of 
plants are identified by a series of obvious characteristics, 
and discover the name (not of that individual as such, but) 
of that kind of plant. In the same way also a classified list 
of symptoms might save a young physician much valuable 
time in diagnosing a disease. 



S^ DIVISION AND CLASSIFICATION. 

A fourth object of classification is to make it easy to deal 
at the same time with things that bear any special relation to 
each other. To this end we put the things themselves or 
their names together. A grocer puts in the same basket all 
the parcels that are to go to the same house ; a lady writes on 
the same list the names of the people or shops to be visited 
on the same afternoon. Here the classification is made for 
an immediate practical purpose — something must be done 
about each of the people or things in question, and the class- 
ified list helps us to do it. But often, and this is the object 
of classification in science, things or the names of things are 
put together because it is desirable to think of them not only 
at the same time but in relation to each other. * Thus chrono- 
logical tables, maps, and astronomical charts are made not 
only to show what happened in a given year or the location 
of a given place, but also to show the general sequence of 
events at any given period, the general conformation of a 
country, the general arrangement of a planetary system. In 
these cases the relations that determine the classification are 
those of time and space, but they may be anything : degree 
of scholarship, in arranging a list of students; degree of 
strength, in a list of acids ; durability, in a list of fabrics or 
dyes ; cause and effect, when the writer on medicine puts to- 
gether all the causes and symptoms of a given disease ; 
means and end, when he adds a list of remedies. 

Scientific classifications are most concerned with relations of 
resemblance and contrast. When a naturalist, for example, 

* It is rather common to speak as though all classification were of 
one's ideas or concepts of things, but this is a blunder. A psychologist 
classifies ideas and feelings when he points out their resemblances and 
differences ; e.g.^ the difference between a feeling of terror and a 
feeling of contempt ; but a naturalist classifies things. It is the business 
of a psychologist to observe the difference between thoughts as such; 
but every other scientist is concerned with the difference between the 
objects that we think of, not the thoughts themselves. To think of the 
difference between things is not the same as to have different thoughts of 
them. 



SCIENTIFIC CLASSIFICATION AND ITS PURPOSES. 53 

classifies all animals into vertebrates and non-vertebrates, he 
merely asserts that each of a certain long list of animals has 
a backbone, and in this respect and certain others that fol- 
low from it resembles each of the others and differs from all 
of those not on the list. 

But what points of resemblance and contrast must be re- 
garded, and in what order, if we are to make a classification 
scientific? The answer to this is that no basis of classifica- 
tion — no fundamenium divisionis — is any better than any other 
in itself. The only general rule is to choose and arrange 
fundamenta divisionis in the way that best shows the points of 
resemblance and contrast in which we are interested or likely 
to be interested. It is just as scientific to classify books by 
their size, publishers, date, color, type, or language as by 
their author or subject-matter, and a great deal more so if 
we are interested in the former and not in the latter. 

If we are not interested in any special characteristic of the 
objects classified the only thing left is to try to get into the 
same class objects that have a great many things in common 
and into different classes objects that have very little in com- 
mon, so ' ' that we shall be enabled to make a maximum 
amount of aggregate assertion with a minimum number of 
propositions." * To do this we must choose as our first 
fundamentum divisionis that point on which the greatest num- 
ber of other noteworthy points of difference depend. It is 
better to divide all living things into animals and plants than 
into those which weigh more than a pound and those which 
weigh less ; because the possession of sensation and the 
power of spontaneous motion f which distinguish animals 
from plants involve innumerable other points of difference, 
while the size involves little or nothing more : to say that a 

* Venn's <' Empirical Logic," Chap. XIII. , to which the reader is 
referred. (Macmillan.) 

\ This of course is the popular distinction. If we wish to be more 
scientific we should say ' the fact that they require protoplasmic food- 
stuff, or cannot decompose carbonic acid gas, which distinguishes,' etc. 



54 DIVISION AND CLASSIFICATION. 

thing is a plant tells a great deal about it ; to say that it 
weighs less than a pound tells hardly anything. 

It is this principle of trying to get into the same class 
those objects which on the whole are most alike that prevails 
in the classification of animals and plants in natural history 
and of books in the subject-catalogues of libraries. 

Any system of classification that regards general resem- 
blance is liable to be upset by an advance in knowledge or a 
change in scientific interests. The common man calls a 
whale a fish, the zoologist says it is not a fish but a mammal, 
because he has found out that on the whole living in the sea 
and looking like a fish involves fewer other noteworthy 
characteristics than suckling the young. In Dewey's Library 
Index illusions are classified with witchcraft and fraud because 
they involve deception, and for the general reader this is 
perhaps the best classification ; but a psychologist would clas- 
sify illusions along with ordinary perceptions, because both are 
interpretations of sensations made in precisely the same way, 
and he knows that the correctness or incorrectness of the 
interpretation, which strikes the layman and upon which 
Dewey's classification depends, is a mere accident and does 
not involve any further differences in the mental processes. 
To illustrate the influence of wider knowledge or deeper 
insight upon a whole system of classification it is only neces- 
sary to point out how the old hard and fast lines between 
genera and species in natural history have been wiped out by 
the theory of evolution, which shows how new species are 
being created continually though slowly by the inheritance 
and consequent accumulation of a vast number of small indi- 
vidual variations. 

The fact that a system of classification is likely to be upset 
by wider knowledge is no reason why it should not be con- 
structed, for a bad classification is better than confusion ; and 
however bad it may be, it is likely to contribute something 
toward the attainment of the wider knowledge by which it 
can be corrected. 



NAMING. 55 

When a classification has been made, the resemblances 
and differences which it indicates can be still further marked 
and more easily remembered and talked about by Naming:. 
the use of class names. The words vertebrate^ ??iaijwial, radi- 
ate, batrachian are all scientific terms invented for this pur- 
pose. But the use of class names was not invented by scien- 
tists, for every common name marks out a class of things 
which it serves to distinguish from all others. Animals and 
plants, trees and grasses, hawks and doves, were distinguished 
and contrasted long before science existed. The scientist, 
as Venn says, usually finds the highest and lowest classes 
of things already made and named. His business is only 
to state their most important difterences distinctly (which 
sometimes involves a correction in the classification of an 
ambiguous kind, such as the whale) and to arrange the inter- 
mediate groups. 



CHAPTER V. 

THE USES OF SINGLE WORDS AND PHRASES. 

We have seen already how to avoid certain gross blunders 
which result from the ambiguity or misinterpretation of words 
and statements ; but if we are to acquire any fine discrim- 
ination in the interpretation and use of language our study of 
words and sentences must not end here. Hence several 
chapters more must be devoted to them. 

To understand the exact meaning of a word in any partic- 
ular sentence it is not enough to know its definition ; for 
however unambiguous the meaning of a word may be as given 
in a dictionary it may be used for any one of several different 
purposes, and if we do not understand the differences between 
these purposes we cannot be sure of interpreting the word 
aright. 

With reference to each one of these different purposes 
w^ords are divided into different classes — usually two; but 
since the same word can be classified with reference to differ- 
ent purposes it can belong to as many different classes as there 
are purposes with reference to which it can be classified. 
We shall see, however, that not every word can be classified 
with reference to all these diff'erent purposes. 

The first division of words which we shall consider is into 
Terms. those that are ' Terms ' , and those that are not. 

A term is a word or group of words used to indicate or 
identify the objects about which a person speaks, or the 
states, qualities, actions or other relations whose possession by 

56 



TERMS. 57 

an object is under consideration. It is, in brief, a name in 
the broadest sense of the word. In the sentence ' The pres- 
ent Emperor of Germany is remarkably energetic ' the first 
five words are regarded as a single term because they are used 
together to point out the individual under discussion ; and 
because the last two words of the sentence are used together 
to indicate a single quality, they also are regarded as a single 
term. In other connections, of course, the words Emperor, 
Germany, energetic, would be regarded as separate terms, 
e.g., The Emperor is energetic ; Germany is a beautiful coun- 
try. Even in the case of the sentence given^ if we should be 
asked to ' define our terms ' it would be proper enough to 
take up the words separately, as they might appear elsewhere, 
and explain that by ' remarkably ' was meant, not ' exces- 
sively', but 'noticeably'; by ^energetic', not 'meddle- 
some' but vigorous'. But if we wished to be absolutely 
accurate, though tedious, we should add to our explanation of 
the meaning of the separate words an explanation of the phrase 
or term as a whole. 

Though every term is a word or combination of words, 
the structure of language is such that some words can never 
be used as complete terms. The object of thought is indi- 
cated y the subject of a sentence ; its relations under dis- 
cussion, by the predicate. Such words as prepositions, con- 
junctions and adverbs cannot be either subjects or predicates 
and therefore they cannot be terms, though they can be parts 
of terms. We cannot say, for example : Of is energetic ; 
nevertheless is very; etc. We can say 'of is a preposition; 
but then the word is used as a noun and is not taken in its 
ordinary sense. Unless a relation is discussed — affirmed, 
denied, or questioned — the word that indicates it is not a 
term. The word ' of in the phrase ' The Emperor of Ger- 
many ' indicates a relation, but it is not a term, because 
nothing is said about the relation it indicates. It merely 
forms a part of the description of the object some other of 
whose relations is discussed. Prepositions joining nouns to 



5 8 THE USES OF SINGLE WORDS AND PHRASES. 

each other, and possessive cases are always devoted to the ex- 
pression of relations which are involved in the conception of 
an object but not discussed. For that reason they can never 
be terms. On the same principle, adjectives are true terms 
when they follow the verb Ho be ' or its equivalents as 
predicates, e.g.^ in the sentence ^ The horse is white', but 
not when they are in their usual position, as in the sentence 
' The white horse kicks '. 

Words which can be used as complete terms are called 
Categoreraatic (Greek, Karrfyopeoo, to assert); those which 
can not, and which therefore can not be used except when 
they are combined into a term with others, are called Syn- 
categorematic (Greek, avv, togetherwith, ?iY\^Karrfyop€Go). 

The distinctions which we have to discuss in the rest of 
this chapter all have reference to terms. We shall therefore 
have nothing more to say at present about syncategorematic 
words. 

The first distinction to be made with reference to terms 
is between those which are used demonstratively and those 

which are used descriptively. By a Demon- 
Demonstra- . , . , 

tive and strative term is meant one that points out an ob- 

descriptive. . i t^ • • ^ ^^ 

ject ; by a Descriptive term, one that tells some- 
thing about it. When we say ^ John is angry ' or ^ That is 
very beautiful', the words ^ John ' and Hhat ' are used 
demonstratively and the remainder of the sentences are 
intended to describe the objects that they point out. The 
word ' John ' is of course a proper name and the word ' that ' 
a ' demonstrative ' pronoun. These parts of speech are de- 
voted so exclusively to pointing objects out, and adjectival 
phrases like ' angry ' and ' very beautiful ' are devoted so ex- 
clusively to their description that if the order of the sentences 
were reversed and we said ^ Angry is John ' or ' Very beauti- 
ful is that ', it would still be plain which words were used to 
point out the objects under discussion, and which were used 
to describe them. 

In the examples just given the subject of each sentence 



DEMONSTRATIVE AND DESCRIPTIVE. 59 

was demonstrative and the predicate descriptive, and by- 
straining matters a little we can say that this is always so. 
We can say, for example, that in the propositions ' A is 
larger than B ', ^ A is bullying B ', everything but the subject 
^ A ' is part of a predicate whose function is merely to de- 
scribe or tell something about A. This, I suppose, would be 
the grammarian's interpretation of the sentences, and it is 
the interpretation that we assumed when we defined the sub- 
ject of a sentence as the name of the object about which we 
are speaking. But it is not quite fair, for in each of these 
sentences we tell quite as much about B as about A. The 
fairer way is to regard the sentence as made up, not of two 
parts, a subject and a predicate, but of three : two demon- 
strative terms, and a third term that describes some relation 
between the things which they point out. In view of this 
interpretation of propositions like these we cannot say that a 
predicate is always descriptive (or even that it always con- 
sists of a single term). But there is nothing in what we have 
said to prevent us from saying that the subject is always de- 
monstrative. If we do say so, however, we must make it plain 
that we are speaking of real subjects and not such nominal 
subjects as * it ' and ^ there ' in propositions like these : ' It 
is a long distance from A to B ' ; ^ It is a long road that knows 
no turning '; ' There is a lion in the way ' . Sometimes, more- 
over, it is hard to tell what is the real subject. In this last 
proposition, for example, are we telling about the lion, as the 
form of the sentence seems to imply, or are we telling about 
the way and why we cannot travel in it ? 

Nouns {i.e., nouns substantive) are usually used demon- 
stratively ; but they can also be used descriptively. When 
we say ' A man came to the house ', the term ^ a man ' is de- 
monstrative, for it points out, rather indefinitely to be sure, 
who it was that came ; but when we say ^ John is a man ', the 
term is used descriptively, for it is intended to summarize 
a great many of John's attributes, to indicate his general re- 
semblance to the other creatures we call men, and perhaps 



6o THE USES OF SINGLE WORDS AND PHRASES. 

to convey an idea of his biological relations to them and to 
other animals. 

Since it is possible to identify an object more or less defi- 
nitely by describing it, a term whose primary function in a 

given sentence is to do the one often serves at 
Connotative . • • , ^ i i i ttti 

andnon-^ the same tmie mcidentally to do the other. When 

we say that a man came to the house we not only 
tell the hearer that one or other of a certain large group of 
things came to the house, but we incidentally describe that 
thing, implying that it has all the qualities and other rela- 
tions of a man ; and when we say that John is a man we not 
only describe him but incidentally we tell that he is one of a 
certain group. Terms which perform this double function 
are called Connotative; those which do not, Non-connota- 
tive.^ 

What words really are connotative and what non-connota- 
tive, and even the definition of these terms themselves, is a 
matter about which logicians are not all agreed ; but the 
distinction will be illustrated well enough for our purposes if 
we say that the ordinary Common Nouns of grammar are 
connotative (^e.g., ^ man ', Miorse ', ^pig'), and that Proper 
Names and Abstract Nouns are probably not. 

Whether a proper name is to some extent descriptive as 
well as demonstrative depends altogether upon whether there 
exists any convention in virtue of which any particular name 
is applied only to certain classes of objects. In English- 
speaking countries nowadays, for example, surnames usually 
indicate family connections. Elsewhere and at other times 
they have indicated something else. A Christian name may 
be given merely because a parent thinks it pretty ; and yet it 
is usually chosen with some reference to sex. Nevertheless 

■^' A ' connotative ' term, as defined in logic, must not be confused with 
the somewhat similar terms ' which have connotation ' as defined in books 
of rhetoric. They both do something incidentally; but this incidental 
function as described in rhetoric is generally some kind of appeal to 
feeling;. 



SINGULAR AND GENERAL. 6 1 

I doubt whether we can say that to that extent it is descrip- 
tive, for however unusual and outrageous it might be to 
name an English boy Mary, one could hardly say that the 
parent who did it had felsely asserted that the child was a 
girl. It need hardly be said that when we call some one a 
Nero or a Socrates or a Napoleon these proper names are used 
altogether in a descriptive sense. 

When a term is used demonstratively — to point out an ob- 
ject of thought — it is said by logicians to be used ^ Denotatively ' 
or in its ' Extension ' ; when used to describe one, it is said to 
be used ' Connotatively ' or in its ' Intension '. From this it 
follows that when we define a term we tell the qualities it con- 
notes ; when we give an example we tell one of the things it 
denotes. As Bosanquet puts it: ^'The denotation of a name 
consists of the things to which it <^/>plies, the connotation 
consists of the properties which it z>/^plies." * 

Proper names are applied (more or less arbitrarily) to some 
individual object for the sake of indicating that particular ob- 
ject as distinguished from all others. But this function can 
also be discharged by some descriptive phrase 
which is obviously applicable to only one particu- and* 
lar object {e.g.^ ' the man at my right ', ' my black 
dog ' ). In either case a term which is intended to discharge this 
function is called Singular. A General term, on the other 
hand, is one applied to every object which possesses some 
given characteristic or characteristics, and used to distinguish 
any object which possesses such characteristic or character- 
istics from objects which do not {e,g. , ' triangle ', ' angular ' ). 

Because a general term is not applicable to an object un- 
less that object possesses a given attribute, it is evident that 
general terms are all connotative. 

Singular terms are intended to distinguish a certain '^real 
essence " , as Locke would have said, a certain person or thing 
that remains that same person or that identical thing through- 
out all the changes it may undergo. 'The thin black- 

^ The Essentials of Logic, p. 88, 



62 THE USES OF SINGLE WORDS AND PHRASES. 

haired man who passes here every morning' — this phrase is 
a singular term, because it is designed for the purpose of 
pointing out a special individual who would remain the same 
person when the description was no longer applicable. For 
the purpose in hand any other description might have done 
as well, for though we may identify the person by means of 
a description, it is the person, not the described characteris- 
tics, that we mean. General terms are intended to distin- 
guish what Locke would have called ^^nonnnal essences" 
from each other. The terms 'a thin man', travellers', 
* good students ', ^ good ', ' gas ' are each applicable to any 
object or set of objects only so long as the objects possess 
the attributes indicated ; they are equally applicable to any 
objects possessed of those attributes, and are chosen for the 
express purpose of calling attention to the presence of the 
attributes. 

Sometimes the same term may be singular in one connec- 
tion (e.g., 'the child is sick'; ' Ccesar was killed '), and gen- 
eral in another {e.g., ' the child is father to the man '; ^ he* is 
a regular Ccesar '~). Thus in logic it is the meaning of a 
word that counts, not the outward form. 

Often a descriptive phrase whose primary purpose is to 
identify an object is not quite accurate, but if it suggests the 
required object this does no harm so far as the identification 
is concerned. If I say that the peddler who was so impudent 
at our door yesterday morning, was afterwards arrested on a 
serious charge, and if you recognize the man from my descrip- 
tion, the description has answered its purpose, even though 
it was not yesterday, but the day before, that he was at our 
door. Sometimes, however, a number of descriptive words 

are added to a demonstrative term when they are 
Epithets. , „ ^ , . , .^ . ' . 

wholly unnecessary for the identification of the 

object, ^.^., ^swift-footed' Achilles, ^ the beautiful and accom- 
plished ' Miss Blank, this ' most dangerous ' disease. Such 
. epithets have a rhetorical value, for they convey in a neat way a 
desired conception of an object about which something is to be 



COLLECTIVE AND DISTRIBUTIVE. 67, 

said ; but no one is logically justified in using one of them if 
its applicability is a question at issue or depends in any way 
upon one. A lawyer, for example, has no right to refer to 
a person accused of murder as ' this brutal assassin ' until after 
the trial is over and the accused is found guilty, and then he 
may not wish to. Such descriptive terms used in this way 
are called Question-begging Epithets. They beg the question 
or take for granted what is to be proved, because they have 
the form and position of descriptive epithets used to identify 
an object; and these nearly always point to qualities tliat are 
obvious and admitted. Question-begging epithets are gener- 
ally intended to appeal to the listeners' emotions and make 
them partisans instead of unprejudiced judges. Thus they 
are doubly unfair. 

When we consider terms from another standpoint we must 
distinguish between those that are qalled Collective (such 
as ^jury', ^army', 'mob', 'herd', 'crew', 
' crowd \ ' heap ' ) and those which are called Dis- and dis- 
tnbutive (such as 'man , 'soldier , 'juryman , 
' goat ' ). A Collective term as distinguished from a Distribu- 
tive is one used to denote any aggregate of similar and 
separable things regarded as constituting some sort of tem- 
porary unit. When all notion of the separateness of the 
individuals in an aggregate is lost, so that the combined whole 
is regarded, at least for the moment, as a true unit, the col- 
lective term which names it become distributive. This is 
most likely to happen when we think of several such aggre- 
gates, e.g.^ 'There were mobs in six cities at once ', ' He was 
convicted by three d i ffe ren t y^/r/i^vT '. 

It is extremely important to distinguish between state- 
ments which are intended to apply to several things con- 
sidered as a wdiole and those intended to apply to each of a 
number of individuals. A jury as a whole cannot get hun- 
gry, though each of its members may. The words 'and', 
'all', 'many' are singularly ambiguous in this respect. 
It was this ambiguity that gave point to the newsboy's re- 



64 THE USES OF SINGLE WORDS AND PHRASES. 

mark : ' Astor and I are worth millions. ' ' Three and 
five ' make eight, not severally but conjointly, while * three 
and five ' are odd numbers severally and not conjointly. 
* They all ' lifted a log conjointly {cuncti'), and ^ they all ' 
told about it severally (^omnes). ^ The mosquitoes in Alaska 
are so large that many of them weigh a pound. ' The terms 
severally and conjointly are often used in legal documents to 
indicate the distinction we are discussing. The most usual 
terms in logic are distrihutively and collectively ."^ 

When we take any of these ambiguous words collectively 
at one stage of an argument and distrihutively at another, it 
is possible to draw conclusions which a fair and 
unambiguous interpretation of the words would 
not warrant, e.g.^ 'All the angles of a plane triangle are 
equal to two right angles ; this is one of them ; therefore 
this angle is equal to two right angles.' 'All the feathers in 
a bed are extremely light ; the bed is made up of all the 
feathers ; therefore the bed is extremely light.' In the first 
of these examples the word ' all ' is taken collectively when 
the premise is admitted, but distrihutively when it is used to 
prove the conclusion, and the fallacy is called one of Di- 
vision. In the second example the word ' all ' is taken dis- 
trihutively in the ambiguous premise when it is admitted, 
but collectively when the premise is used to prove the con- 
clusion, and the fallacy is called one of Composition. f 

* Both Jevons and Minto contrast Collective terms with General terms. 
Jevons says '' We must carefully avoid any confusion between general 
and collective terms " (p. 19) ; and Minto speaks of " Collective names 
as distinguished from general names " (Logic, p. 58). In each case, 
however, it seems to be an oversight, for in the exercise at the end of the 
chapter Jevons says the reader is to determine whether a term is <' collec- 
tive or distributive ", not collective or general. So with Minto, most col- 
lective names fall under his definition of general names (see p. 44). 

A collective term may be either singular or general, e.g.: The Smiths 
have a new house (singular) ; he was attacked by a mob (general). 

\ A good many fallacies, such as the stock argument for protective 
tariffs, are credited by Whately, Jevons, and others to this confusion, 



ABSTRACT AND CONCRETE. 05 

A more serious danger than that just mentioned is that 
when we use collective terms we shall forget that the indi- 
viduals in the group are not a real unit, but can be consid- 
ered as one for certain purposes only. I give one example 
of this fallacy here. There will be others in a later 
chapter. 

^' During the last ten years I have read a great many 
books and articles, especially by German writers, in which 
an attempt has been made to set up ' the State ' as an entity 
having conscience, power, and will, sublimated above human 
limitations, and as constituting a tutelary genius over us all. 
I have never been able to find in history or experience any- 
thing to fit this conception. . . . My notion of the State 
has dwindled with growmg experience of life. As an ab- 
straction, the State is to me only AU-of-us. In practice — 
that is, when it exercises will or adopts a line of action — it is 
only a little group of men chosen in a very haphazard way by 
the majority of us to perform certain services for all of us. 
The majority do not go about their selection very rationally, 
and they are almost always disappointed by the results of 
their own operation. Hence Hhe State ', instead of offering 
resources of wisdom, right reason, and pure moral sense be- 
yond what the average of us possess, generally offers much 
less of all those things. ' ' ^ 

From another standpoint terms are divided into Abstract 
(such as ^redness', ^ anger', ^kindness') and Concrete 
(such as ^red', ^ angry man', ^kind'). Ab- 
stract terms are nouns used to indicate the quali- and 

, , . r ^ • concrete, 

ties, states, acts, or other relations of things. 

They are ^Abstract' because, unlike adjectives and verbs, 
they can be used grammatically without any mention of the 
thing to which the qualities and so forth belong and without 



when, so far as I can see, they have absolutely nothing to do with it. 
have treated of them elsewhere. 

* Sumner, "What Social Classes Owe to Each Other ", pp. 9, 10. 



66 THE USES OF SINGLE WORDS AND PHRASES. 

which these latter could not exist. We can say, ^ Anger is 
foolish', or ' A man is foolish to be angry ', but not ^ Angry 
is foolish ' . Abstract terms thus seem to ^ abstract ' or draw 
away one's thought from things. 

Every term which is not abstract is called Concrete. Con- 
crete terms are therefore (i) the names of things, or (2) 
adjectives or verbs, that is to say, names of relations which 
cannot be used grammatically without any mention of the 
thing to which they belong."^ 

The value of abstract terms lies in the fact that through 
their use attention can be called more briefly and more effect- 
ively than in any other way to certain features of things 
which we wish to discuss without any special reference to the 
things themselves. It is easier, and on the whole more effec- 
tive, to say ' Self-sacrifice deserves gratitude ' than to say 
' When a person acts in such a way as to injure himself because 
he wishes to benefit some one else, the person whom he meant 
to benefit ought to feel grateful, no matter who the persons 
may be ' . But in spite of the great value of abstract terms, 
there is no more important practical rule in logic than that 
which says Beware of abstractions ! 

The danger involved in the use of abstract terms is due to 
the fact that such terms are always nouns and that nouns are 

usually the names of things. We are therefore 
Hyposta- ^ , , ^ ,. 

Using ^ very prone to regard the quality or relation re- 
ferred to by an abstract term as a sort of //iing 
wilh a certain independent existence, possessing attributes and 
playing an active part in the world as things alone can. In 
this way ^ life ', ' natural laws ', ' motion ', ' force ', ' ideas ', 
^justice', ^evil', * the Zeitgeist ', 'Public Opinion', and a 
host of other abstractions are liable ^' to play the part of sham- 
essences, and cheat their way into recognition as realities." f 

^ The word ' thing ' is intended here and is usually intended elsewhere 
in this book to refer to whatever possesses substantial reality. It there- 
fore includes persons. 

f Jas. Martineau, " Study of Spinoza ", p. 12, 



HYPOSTATISING ABSTRACTIONS. 67 

Nothing exists in the whole universe but a vast number of 
persons and things acting in various ways. Tt has no place 
for abstractions. To say that a person has an idea means 
that he thinks. To say that a speaker conveys an idea to 
his hearers means that he makes them know what he thinks. 
To say that a smile spread through the company means that 
several persons smiled at once, or that some smiled and 
then others smiled because they saw them do it. To say 
that energy is stored up means that a thing is not acting, 
but is in a condition to act, upon occasion. To say that 
motion is transmitted means that one thing stops moving and 
another begins. Imagine a smile spreading through a com- 
pany like water through a sponge, or energy stored up 
like grain in the inner recesses of a thing, or motion being 
carried from its resting-place in one thing to a quiet nook in 
another ! Public opinion is only what is similar in every- 
body's w^ay of thinking about a question. A law is nothing 
but a statement of how people must act if they wish not 
to be punished by the law-maker, or a statement of how 
things as a matter of fact do act under certain circum- 
stances. It is not some shadowy reality existing before or 
apart from all things and compelling their obedience by its 
own strength. A law is never imposed on things. To say 
that two chemicals have an affinity for each other does not ex- 
plain why they combine or act in conjunction; it merely 
states the fact that they do. — And so of all the rest. 

The habit of defining abstract nouns rather than their cor- 
responding verbs and adjectives helps to entrap us in this 
^' snare of abstractions". We have been taught to say that 
attraction is the principle or power in virtue of which one 
body approaches another, or that beneficence is the trait of 
character manifested in acts of general kindness. It would 
be better to say that one thing attracts another when it makes 
it come nearer, and that a person is beneficent when he is 
kind to everybody. '^The snare of abstractions concealing 
itself chiefly in common nouns, we shall best guard against it 



68 THE USES OF SINGLE WORDS AND PHRASES. 

by admitting to our definition no substantive where an adjec- 
tive [or verb] ought to serve as well." ^ 

It is often said that the tendency to take abstractions for 
things is particularly characteristic of philosophers. This is 
probably not true. And yet the philosopher must take spe- 
cial care to overcome it; for the nature of his work is such 
that a very few blunders of this kind can spoil it. Hence 
the advice contained in the following quotation is excellent, 
and the criticism implied in the last sentence is not altogether 
unjust: ''If the student of philosophy would always, or at 
least in cases of importance, adopt the rule of throwing the 
abstract language in which it is so frequently couched into a 
concrete form, he would find it a powerful aid in dealing with 
the obscurities and perplexities of metaphysical speculation. 
He would then see clearly the character of the immense mass 
of nothings which constitute what passes for philosophy." * 

Philosophy, however, is not the only subject that sufi'ers by 
this tendency to take abstractions for things, as can be shown 
by the following passages from Langlois and Seignobos' beau- 
tiful '^ Introduction to the Study of History ", already quoted. 

''The facts of society are of an elusive nature, and for the 
purpose of seizing and expressing them, fixed and precise 
language is an indispensable instrument ; no historian is com- 
plete without good language. It will be well to make the 
greatest possible use of concrete and descriptive terms : their 
meaning is always clear. It will be prudent to designate 
collective groups only by collective, not by abstract names 
(Royalty, State, Democracy, Reformation, Revolution), and to 
avoid personifying abstractions. We think we are simply 
using metaphors, and then we are carried away by the force 
of the words. Certainly abstract terms have something very 

* Martineau. loc. cit. p. 124. Lotze somewhere says about the same 
thing. See also the introduction to Berkeley's "Principles of Human 
Knowledge ". 

■f- Bailey's ''Letters on the Mind", vol. ii, p. 159, quoted by Bam, 
''Logic", p. 53. 



IIVrOSTATISING A]>,Sin>lACTIOXS. 69 

seductive about them, they give a scientific appearance to a 
proposition. But it is only an appearance, behind which 
scholasticism is apt to be concealed ; the word, having no 
concrete meaning, becomes a purely verbal notion (like the 
soporific virtue of which Moliere speaks)." (Pp. 266-7). 

^^Specialists, influenced by a natural metaphor, and struck 
by the regularity of these successions, have regarded the evo- 
lution of usages (of a word, a rite, a dogma, a rule of law), 
as if it were an organic development analogous to the growth 
of a plant ; we hear of the ' life of words ', of the ^ death of 
dogmas', of the 'growth of myths'- Then, in forgetfulness 
of the fact that all these things are pure abstractions, it has 
been tacitly assumed that there is a force inhering in the 
word, the rite, the rule, which produces its evolution. . . . 
Just as usages have been treated as if they were existences 
possessing a separate life of their own, so the succession of 
individuals composing the various bodies within a society 
(royalty, church, senate, parliament) has been personified by 
the attribution to it of a will, which is treated as an active 
cause. A world of imaginary beings has thus been created 
behind the historical facts, and has replaced Providence in 
the explanation of them. For our defence against this de- 
ceptive mythology a single rule will suffice : Never seek the 
causes of an historical fact without having first expressed it 
concretely in terms of acting and thinking individuals. If 
abstractions are used, every metaphor must be avoided which 
would make them play the part of living beings." (Pp. 
288-9.)* 



* Abstract terms are often demonstrative rather than descriptive. To 
be sure, they point out qualities and relations which have no independent 
existence and which are usually best indicated by descriptive terms; but 
whether the qualities or relations in question have such an existence or 
not, they can be the objects of thought, and when they are, the words 
used to point them out are demonstrative. Indeed we may go so far as 
to use a demonstrative term to indicate a quality, actor relation and 
a descriptive term to indicate the real thing without which it could not 



70 THE USES OF SINGLE WORDS AND PHRASES. 

The term ^Abstract' is often applied, with a somewhat 

broader meaning than that given in the definition, to words 

which indicate complex relations that are not eas- 
Secondary 
meaning: of ily perceived by the senses. Thus we might say 

that when the words ' free ' and ^ equal ' are used 
to mean ' not tied or locked up ' and ^ of the same size ' they 
are concrete ; but when they are used ( ^ in the second inten- 
tion ') to mean what politicians mean when they say that all 
men are born ' free and equal ' they are abstract. The first 
relations can be easily perceived by the senses and easily 
defined ; the second can not. In the same way the terms 
^universe', * siderial system', &c., might be called ab- 
stract.^ 

General terms are used to distinguish objects which possess 
certain characteristics from those which do not. They are 

exist, as when we speak of ' Asiatic duplicity ', ' the Turkish atrocities ', or 
' the Franco-German war'. 

* Abstract and Concrete words are often distinguished by their form ; 
but " unfortunately " the two forms '* are frequently confused, and it is by 
no means always easy to distinguish the meanings. Thus * relation * 
properly is the abstract name for the position of two people or things to 
each other, and those people are properly called 'relatives' (Latin rela- 
tivus^ one who is related). But we constantly speak now of ' relations *, 
meaning the persons themselves ; and when we want to indicate the ab- 
stract relation the}^ have to each other we have to invent a new abstract 
term, ' relationship '. ' Nation ' has long been a concrete term, though 
from its form it was probably abstract at first ; but so far does the abuse 
of language now go, especially in newspaper writing, that we hear of a 
' nationality ' meaning a nation, although of course if • nation ' is the 
concrete, ' nationality ' ought to be the abstract, meaning the quality of 
being a nation. Similarly ' action', 'intention', 'extension', 'conception*, 
and a multitude of other properly abstract names, are used confusedly 
for the corresponding concrete, namely ' act ', ' intent ', ' extent ', ' con- 
cept ', etc. ' Production ' is properly the condition or state of a person 
who is producing or drawing something forth ; but it has now become 
confused with that which is produced, so that we constantly talk of the 
' productions ' of a country, meaning the ' products '. . . . Much injury 
is done to language by this abuse" (Jevons, "Elementary Lessons in 
Logic ", p. 21). 



POSITIVE AND NE(;ATIVE. 71 

usually applied to the objects which possess tlie characteristic 

in question, but they can be so altered as to ap- 

, 1 1, i-rr 1 ' 1 Positive 

ply — or wholly different terms can be invented and 

necativc. 
which apply — only to the objects which do not 

possess the characteristic in question. General terms of the 
first sort are called Positive, those of the second sort Negative. 
The words ^ Jew ', ^ Greek', 'citizen', 'clergyman', 'edu- 
cated', 'Aryan', 'white', are positive terms. Their cor- 
responding negatives are 'Gentile', 'barbarian' (in the 
earlier sense of the word), 'alien ', ' layman ', ' uneducated ', 
'non-Aryan', 'not white'. Where negative terms do not 
exist they can always be made by attaching some such prefix 
as 'in-', 'un-', 'non-', or 'not-', or some such suffix as 
'-less ' to a positive term ; but we must not take it for granted 
that terms which have these affixes always correspond in 
meaning in this way with those that have not. It is said that 
a college chaplain once became sleepy during a service and 
implored the irreligious to become religious ; the immoral, 
moral ; the intemperate, temperate ; the inebriate, ebriate ; 
and the indifi'erent, different ! 

Sometimes terms which are negative in form have a positive 
meaning, and vzce versa. Thus the terms ' uncomfortable ' , 
* unhappiness ' , 'uneasiness', are all used to indicate that 
disagreeable feelings are present, and, on the other hand, 
the terms 'free', 'sober', and 'healthy' are used to indi- 
cate that certain undesirable conditions are absent. The 
terms ' moral ' and ' good ' are probably more often used in 
a negative sense than in a positive. 

Though negative terms are used to indicate the absence of 
certain characteristics, they are not properly applicable to 
everything which does not possess these characteristics. A 
mutton-chop is neither a Jew nor moral nor able to see, but 
neither is it a Gentile nor immoral nor blind. A man, on 
the other hand, must be one or the other. Negative terms 
are thus only applicable to things that are capable of posses- 
sing,, or might reasonably be supposed to possess, the char- 



72 THE USES OF SINGLE WORDS AND PHRASES. 

acteristics whose absence the negative term denotes. They 
are used with reference to Avhat De Morgan has called a 
Umited universe of discourse. Within that universe, but not 
beyond it, everything can be described either by a positive 
term or by the corresponding negative. In the example just 
given the universe of discourse was human beings. If we say 
that everything must be either light or heavy, here or there, 
we have in mind the universe of tangible objects existing in 
space. The statement would not be true of a soul or a 
feeling of remorse. When Euclid says that things which are 
equal to the same thing are equal to one another, his universe 
of discourse is the size of lines or figures. If A is equal to B 
in social position and B is equal to C in intelligence, it does 
not follow that there is any respect in which A is equal to C. 

There are a vast number of w^ords whose meaning is 
ambiguous until one knows the universe of discourse to which 
they refer. The term ' irregular ' , for example, may have 
reference to the distribution of lines in space, or the succes- 
sion of events in time, or a person's moral relations. 

Which of two mutually exclusive terms, one or other of 
which is applicable to every individual in a given universe of 
discourse, is to be regarded as negative is often a matter of 
indifference, for within a given universe the absence of one 
characteristic involves the presence of another belonging to 
the same general class. A substance which is immaterial 
must be spiritual, a thing which we take the trouble to 
describe as not white is usually a kind of thing that must 
have some color or other. There is as much fulness of 
determination — there are as many attributes — in one case as 
in the other. 

Though ^ immaterial ' and ^ not white ' are both terms 
which imply the presence of some corresponding attribute, 
there is this difference between them : in the one case we 
know immediately what the attribute is — the thing must be 
spiritual ; in the other we do not, for the thing may have any 
one of many colors. Thus when there are only two alterna- 



RELATIVE AND ABSOLUTE: EIRST SENSE. 73 

tives, a term which indicates the absence of one of them lias 
a definite positive significance; when there are many the pos- 
itive significance is indefinite. 

A positive term and its negative are called with reference 
to each other negative, contradictory, or more properly, con- 
trapositive terms. 

Some terms (such as ' giant ' , ' dwarf ' ; ' immense \ ' tiny ' ; 
' courageous ', ' cowardly '; ^ noble \ ' ignoble ') are used 
to name contrasting and mutually exclusive relations; but 
there are objects in the universe of discourse to which neither 
term in such a pair is applicable. There are many men 
who are neither giants nor dwarfs, many acts that are neither 
noble nor ignoble. In such cases the terms are not Con- 
tradictories, but contraries or oppo sites. 

Whether such terms as ' thin ' and ' thick ' , ' large ' and 
^ small ' are contrary or contradictory depends upon the circum- 
stances in which they are used. The frequent controversies 
to which they give rise in this respect are due to the fact that 
they are never terms of precision in any respect. When we wish 
to be accurate we give measurements. Neither speaker nor 
hearer usually stops to ask what size a thing must be in order 
to be large or small; they therefore do not ask whether there 
can be anything of the kind discussed which is neither large 
nor small. To raise the question is to attempt to render 
definite the meaning of terms whose value lies in their essen- 
tial vagueness. Hence the old catch called Sorites : ' How 
many things does it take to make a heap ? ' 

The last distinction between terms which we shall have to 
consider is between Relative and Absolute. Unfortunately 
there are two distinct senses in which a term 
can be said to be relative. In the first sense of atosoiate : 

fifSt S6I1S6. 

the word a term is called Relative when (as 
with * master ', ^combatant', Mover') it is applied to a 
person or thing to mark a certain active relation to some 
other person or thing *, — a relation which might have been 
■^ These relative terms are usually nouns or words used as such, e.g.^ 



74 THE USES OF SINGLE WORDS AND PHRASES. 

expressed by a transitive verb or a phrase involving one. 
Such names are usually found in pairs called correlatives^ one 
for each party to the relation^ ^-g-, ^master', 'servant'; 
Mandlord', 'tenant'; 'debtor', 'creditor'; 'victor', 
' vanquished ' ; ' lover ', ' beloved '. 

We might avoid the use of such terms by saying that one 
person works for another, or has rented his house, or has 
borrowed money from him and not yet paid it back, and so 
forth. In a world in which nothing affected anything else 
this first kind of relative terms would have no place. They 
express a relation existing only between two active beings. 
Relative terms of the second kind, on the other hand — of 
which we are about to speak — express no action of one thing 
upon another, but merely the fact that some one has com- 
pared them in a given respect. 

In the second sense of the word terms are called ' Relative ' 
when, like such words as 'larger ', they indicate the result of 
Second ^ comparison with some standard which the term 

sense. itself does not indicate. The most obvious ex- 

amples of such terms are adjectives of the comparative de- 
gree, for with them it is necessary to name the standard in 
some added words in order to give the term any meaning, 
e,g, , ' A robin is larger than a sparrow \ With superlatives we 
recognize that a standard is involved though we do not always 
mention it, e.g. , ' I saw the loveliest picture '. Such expressions 
as ' rather beautiful ', 'very beautiful ', ' extremely beautiful ', 
'most beautiful' (not distinguished in Latin from ordinary 
comparatives and superlatives) also involve some reference to 
a standard. By a ' rather beautiful ' thing we mean one that 
is perhaps somewhat more beautiful than the average of its 
kind ; by an ' excellent ' piece of work, one that is exception- 
ally good. 

my beloved. They are perhaps occasionally adjectives : e.g., parental, 
though I am not sure whether this should really be called a relative term 
or not. They are almost always applied to persons, though not always : 
e.g.^ reagent. 



SECOND SENSE. 75 

It is less obvious, but no less true, that an immense number 
of terms ' positive ' in form are really used in a comparative 
or relative sense. A large thing is larger than a small thing, 
a clean thing cleaner than a dirty thing, an intelligent creature 
more intelligent than a dull one ; but a large rat is not neces- 
sarily larger than a small elephant, a clean stable cleaner than 
a dirty table-cloth, or an intelligent horse more intelligent 
than a dull man. In each of these cases the name of the 
thing to which the adjective is applied indicates the standard 
of comparison. A large rat is one larger than most other 
rats ; an intelligent horse, one more intelligent than most 
other horses ; a clean stable, one cleaner than most others, 
or as clean as one could reasonably hope to keep a stable. A 
rat is an animal, but we cannot say that a large rat is a large 
animal, because the standard of largeness changes as we pass 
from the consideration of rats to that of animals in general. 
What we have a right to say is that a large rat is an animal 
larger than most rats. In this way we retain the meaning of 
the word ' large ' with which we started. 

Amongst other kinds of inference Jevons mentions Imme- 
diate Inference by added Deter mma7tls, which ^^ consists in 
joining some adjective or similar qualification 
both to the subject and predicate of a proposition. ' ' 
Hyslop says of it that terms expressing quantity, such as 
Marge', Mong ', ^ small', ^ short', must be used carefully; 
but that terms expressing quality ^^can be used with perfect 
freedom, provided they are not used equivocally".* If 
more examples are needed to show that this is not the case 
there are plenty to be had. An Australian Bushman is a 
man, but an intelligent Bushman is not an intelligent man, 
a respectable saloon is hardly a respectable place, an ener- 
getic snail an energetic animal, nor a fast mule-car a fast 
means of transportation. 

This ^ inference by added determinants" gives a good 

* Elements of Logic, p. i68 (Scribners, 1894. Third Edition), 



76 THE USES OF SINGLE WORDS AND PHRASES. 

illustration of the trouble we get into when we substitute rules 
of verbal manipulation for thought about the things that the 
words are intended to denote. 

The following passage from Schopenhauer shows how even 
a first-class author is likely to deceive himself and his readers 
when he makes too much use of relative terms. The passage 
seems to be full of meaning, but it turns out on analysis to be 
absolutely empty. 

'^This human world is the kingdom of chance and error. 
. . . [i] Everything better only struggles through with 
difficulty; what is noble and wise seldom attains to expres- 
sion, becomes effective and claims attention, but [2] the 
absurd and perverse in the sphere of thought, the dull and 
tasteless in the sphere of art, the wicked and deceitful in the 
sphere of action, really assert a supremacy, only disturbed 
by short interruptions. On the other hand [3] everything 
that is excellent is always a mere exception, one case in 
millions, and therefore if it presents itself in a lasting work, 
this, when it has outlived the enmity of its contemporaries, 
exists in isolation, is preserved like a meteoric stone, sprung 
from an order of things different from that which prevails 
here.">l< 

These words mean something like this : ^ I am dissatisfied 
with the w^orld because [i] the exceptionally good is excep- 
tional, [2] what is no better [and no worse] than the com- 
mon is common, and [3] anything good that is exceptional 
enough for me to call it excellent is very exceptional indeed.' 
If the value of everything in the world were increased a 
thousandfold a new philosopher who happened to feel dis- 
satisfied could use Schopenhauer's very words, for ^ good ' 
and ^ bad ' would be interpreted then as they are now with 
reference to the average. 

^- '^The World as Will and Idea", Vol. I^ p. 417 (Kegan Paul, Trench, 
Triibner & Co., 1891). 



CHAPTER VI 

THE RELATIONS EXPRESSED IN PROPOSITIONS 

The meaning of words and statements has been discussed 
enough in the foregoing chapters to guard against various 
kinds of rather gross blunders. Our next task is to inquire 
what fundamental relations of things statements of various 
kinds imply. This is the work of the present chapter. In 
the next we shall carry the same subject further by inquiring 
what any proposition implies about the existence of the 
things it mentions. After these more general discussions 
we shall come back and consider propositions from a more 
formal standpoint, taking up the difference between various 
forms of statement, the significance of each, and the way in 
which a statement in one form of words may imply the truth 
or falsity of a statement in some other form of words. 

* This ts John ' ; ^ John is happy ' ; ^ John is riding a horse *. 
It is perfectly evident that in these propositions the rela- 
tions expressed by the verb ' is ' are wholly different and 
incomparable. In the first case it helps to identify 
a person ; in the second, it helps to tell something fundamental 
about his state of mind ; in the third, it helps to 
tell his relation to something else. How many absolutely 
different kinds of relation we can think of and express in 
propositions it is hard to say. The question is one whose full 
discussion belongs to metaphysics rather than to logic ; and 
it is one about which metaphysicians have not agreed. 
Nevertheless, something should be said about it here ; for the 

77 



73 THE RELATIONS EXPRESSED IN PROPOSITIONS. 

very first rule of logic is to understand the meaning of the 
words we use. 

In thinking about the question it is well to remember that 
in reality nothing exists but things (including persons) with 
their various attributes and acts. The following list is per- 
haps as good as any. 

1. We are able, first of all, to distinguish between various 
individual things and to recognize the fact that through all 
the changes they undergo each one of them remains the 
same : the Paul who preached Christ was identical with the 
Saul who was present at Stephen's death, in spite of his 
change of heart and name in the meantime; the rock on 
Emerson's grave to-day is the very same rock that was there 
yesterday and that was carried there years ago. Precisely 
what it is that makes a thing to be the same throughout all 
its changes of state and circumstances, — whether the ship of 
Argos, repaired so often that at last none of the original 
material remained, was really the same ship or not, — this is 
a detail of metaphysics which we cannot discuss here. But 
in a general way every one knows what it is to recognize an 
old friend, or to say that he himself is the ve?y person who 
performed such and such an act, or that the book in his 
hand is not the one he bought yesterday, though the two look 
precisely alike. 

The first kind of proposition, then, is that which asserts or 
denies this unity or individual identity of a thing that then 
was there or did that, with one that afterwards was here or 
did this. 

It is evident that any proposition of this kind must in- 
volve two demonstrative terms connected by the verb to be, 
e.g., This — is — the man who was here yesterday. 

2. The second kind of relation .afiirmed or denied by 
propositions is that which exists between a thing and its 
qualities, states, or activities (whether we suppose it to be 
conscious of these or not); in short, it is a relation of subject 
and attribute, e.g.: ' Bulldogs are courageous ' ; ^ this iron is 



FIVE FUNDAMENTAL RELATIONS. 79 

not cold ' ; ^ he laughed ' ; ^ he is asleep' . The subject of such 
propositions is always a demonstrative term ; the predicate is 
always descriptive, but its meaning may be expressed either 
by the verb to he or its equivalent {i.e., to seem, to appear, or 
some other similar verb) followed by an adjective or its 
equivalent {i.e., some descriptive noun or phrase), or merely 
by an intransitive verb (with or without a completing or 
modifying adverb), e.g.\ ' He is insane'; '\\q is a lunatic '; 
^ he raves '; ^ he acts insanely '. 

3. The third kind of relation affirmed or denied by propo- 
sitions is the action of one thing upon another, or the mutual 
relations of two things as active beings. Propositions ex- 
pressing such relations involve two demonstrative terms and 
a transitive verb or its equivalent, e.g.: ^ John strikes his 
horse'; ' A. and B. are quarreling '; ^ C. is D.'s landlord', 
i.e., rents a house to him; ^ E. wattis on the grass', i.e., 
treads the grass. These relations may be called causal or 
dynamic. 

Whether a proposition belongs to this third class or to the 
second is often a mere question of interest. A man cannot 
walk without treading upon something, but we are not usu- 
ally interested in the effect upon the object beneath his feet, 
and so we regard the statement that he walks as merely 
descriptive. When we are interested enough to tell what 
he walks upon the dynamic relation becomes prominent. 
Further, as Sigwart says in his '■' Logic ": * " When a man 
walks he moves his legs ; that which from one point of view 
is mere action appears from another as an effect upon his 
limbs, which are relatively independent things." Here, 
again, the classification of the proposition depends upon the 
interest which one can reasonably be supposed to take in 
some particular aspect of the whole fact stated. 

Sometimes, but not usually, it is proper to regard a state- 
ment of a thing's color, taste, smell, or other perceptible 

* Vol. I, p. 37 (Macmillan) 



So THE RELATIONS EXPRESSED IN PROPOSITIONS. 

quality as dyimmic rather than merely descriptive ; for to 
have a certain color is to reflect light in a certain way, and 
to have a certain smell is to act chemically in a certain way 
upon an olfactory organ. But when the ultimate nature of 
things is not under discussion it is more convenient to ignore 
these facts and regard such statements as merely descriptive. 
. 4. Propositions of the fourth kind affirm or deny the exist- 
ence of various non-dynamic or non-causal relations between 
two or more different things or other objects of thought. 
They express our comparisons between them rather than the 
action of one upon another. We may say, for example, that 
several objects are st/m'/ar or dissimilar; that things or events 
coexist or succeed each other in time ; that they bear to each 
other various relations in space ; that one thing is more or less 
beautiful, one musical note 'higher'' or ' lower \ or one man 
morally better or worse than another, without supposing the 
objects whose relations we discuss to affect each other in any 
way whatever. The number of relations of this kind which 
anything bears to anything else is limited only by the ability 
of beings that know them both to compare them together in 
various respects ; and whether many or few such relations be 
discovered or exist has not the slightest effect upon the 
things compared or their activities. Causal relations, on the 
other hand, engross more or less of a thing's energy, and 
may thus interfere with each other. Anything, A, might 
resemble B, coexist with C, be heavier than D, lighter than 
E and beside F, all at once ; but if A were a man he could 
not at any one time fight with B, dance with C, and discuss 
philosophy with D. Causal relations exist directly for the 
things related, and seem to penetrate into and afl'ect their 
inmost being ; non-dynamic relations concern nothing and 
nobody but the being that discovers them. 

The most important of the non-dynamic relations are 
those of Space and Time, without which the mathematical 
sciences would be impossible. They are so important that 
many eminent writers give them a separate place in their 



FIVE FUNDAMENTAL RELATIONS. 8 1 

lists of relations. Indeed relations of time and space are 
often supposed to comprehend causal relations. The ques- 
tion is one of metaphysics which cannot be discussed here.* 

When we speak of the color or of any other attribute of an 
object as identical with that which exists elsewhere, the rela- 
tion asserted is really a relation of resemblance rather than of 
individual identity. We merely mean that the similarity- is 
complete. We must not be deceived by a merely verbal 
resemblance between two propositions. If I say that your 
clothes are the same as mine the relation in question is one of 
resemblance ; if I say that they are the same that you wore a 
year ago the relation is one of identity. If I say the house has 
the same color it had ten years ago the relation indicated by 
the word ' same ' is one of similarity ; if I say it has the same 
paint the relation is probably intended to be one of individual 
identity. The dis^tinction here pointed out between the same 
thing and the same kind of thing is very important, though 
sometimes lost sight of, in metaphysical discussions. In which 
sense, for example, do we see the same rainbow when the sun 
comes out again, and have the same idea or make ^ the very 
same ' remark as somebody else ? 

5. So far we have discussed the various relations which exist 
between the things we know or think about, but we have said 
nothing about our knowledge of these relations. It is one 
thing for the frog that exists to-day to be identical with the 
tadpole that existed six months ago, and quite another thing 
for you or me to recognize that it is identical ; one thing for 

■^ It may occur to the reader that the non-dynamic relations between 
several objects can be affirmed or denied only because the things com- 
pared act upon the person making the comparison, e.g.^ that we say one 
thing is prettier than another because it acts upon our senses in such a 
way as to give us more aesthetic enjoyment. This is often the case, but 
we must not infer from it that the non-dynamic relations can be resolved 
into dynamic, for even if we suppose that to be pretty means merely to 
please the beholder, in the example given there is still a comparison ex- 
pressed between the amount of enjoyment present in the two cases. We 
cannot therefore get rid of the element of mere comparison. 



82 THE RELATIONS EXPRESSED IN PROPOSITIONS. 

a man to be angry, and quite another thing for us or even for 
the man himself to know that he is angry ; one thing for A to 
be larger than B, or to be near B, or to influence B, and quite 
another thing for us to know or think about these relations. 

We have thus a new kind of relation to deal with, namely, 
that between a person thinking and the thing he thinks about 
— between thought and its object. This relation can be called 
noetic. 

This noetic relation, or relation between thought and its 
object, can be affirmed or denied like any other: e.g,^ I was 
thinking of you ; I love you or fear you ; I do not desire a 
certain end ; he knew, or was mistaken, or was doubtful about 
a certain matter ; your ideas about it are consistent, or con- 
tradictory, or absurd ; he is right about it; he thought he 
knew ; I mean you. In all these cases something is said 
about some aspect of the relation between a thinker or his 
thought and the object thought about. 

In the history of philosophy much has been made of the 
distinction between real and verbal propositions (otherwise 
called Synthetic and Analytic, Ampliative and Explicative, 
Accidental and Essential) . A Real proposition tells something 
about an object, e,g. : 'A thrush is in the tree', ^ TuUy is 
dead ' . A Verbal proposition tells the meaning or part of the 
meaning of a word, e.g. : ' A thrush is a kind of bird ', ' Tully 
is Cicero '.* Every definition is thus a verbal proposition. 
Euclid's definitions are supposed to be merely verbal — telling 
nothing more than the meaning of words ; his axioms and 
postulates to be real — telling something more than the names 
of various figures strictly imply, though perhaps not more 
than everybody knows. Real propositions may belong to any 
one of our fi\Q classes. Verbal propositions are always 
noetic ; for to tell the meaning of a word is to tell of what I 

* Contrast with these propositions such a one as this: 'That man's 
name is Washington Jefferson Madison Stokes '. Here the name is re- 
garded as a kind of appendage, and the proposition is as descriptive as 
if it had been said that the man had thirteen fingers, 



FIVE FUNDAMENTAL RELATIONS. 83 

am thinking and of what I wish my hearer to think when I 
use it.* 

It is probable that we can never speak or think of a relation 
not included in this list : Individual Identity, Subject and 
Attribute, Causal relations between several things, Non-dy- 
namic, or Non-causal, relations between several things, and 
relations between thought and its object or Noetic relations. 
These then are the so-called categories ; but it must be remem- 
bered that the fourth class includes a great many different 
relations which agree in only one respect, namely, that they 
involve at least two objects without involving any action of 
the one upon the other, f 

* The terms Real and Verbal seem to me preferable to Kant's Syn- 
thetic and Analytic, partly because as Mansel says, ''propositions in which 
the predicate is a single term synonymous with the subject" cannot pos- 
sibly involve any analysis or splitting up of the meaning of the subject; 
e.g.^ Tully is Cicero (see Keynes, "Logic ", p. 43, 3d ed.) ; but mainly 
because the term Analytic implies that both subject and predicate of 
verbal propositions are always used in a connotative or descriptive sense 
and that the function of such propositions is to analyze ideas rather than 
to identify things spoken of. In a word, Kant's terminology does not 
suggest any clear distinction between thought and its object. 

f Aristotle's list of categories is as follows: Substance, Quantity, Qual- 
ity, Relation, Action, Passion, Place, Time, Posture, Habit. 

Hume gives Resemblance, Identity, Space and Time, Quantity or 
Number, Degree of Quality, Contrariety, Cause and Effect. 

Kant gives Space and Time and four sets of 'pure conceptions ', viz., 
Quantity, including Unity, Plurality, Totality; Quality, including Real- 
ity, Negation, Limitation ; Relation, including Substance and Accident, 
Cause and Effect, Reciprocity between the active and the passive; 
Modality, including Possibility and Impossibility, Existence and Non- 
existence, Necessity and Contingency. 

Mill gives Sequence, Coexistence, Simple Existence, Causation, Re- 
semblance. 

For an explanation of Aristotle's list see Minto's " Logic ", Chap. III. 
Hume's categories, called by him "philosophical relations ", are enumer- 
ated and explained in the "Treatise of Human Nature", Bk. I, Pt. I, 
Sec. V. But his discussion of Space and Time and Causation runs 
through the first three ' Parts '. Kant's categories, which he makes to 
correspond with the formal differences between propositions as set forth 



§4 THE RELATIONS EXPRESSED IN PROPOSITIONS. 

Since abstract propositions can always be reduced to con- 
crete, it is evident that no new class of relations need be made 
on their account. 

Though these relations are probably all we can think of, 
they are often so combined as to give the appearance of some- 
thing quite different from any of them. The rela- 

comMned tion of means and end, for example, is made up of 
relations. , . - i • / • i • \ i 

a desire lor somethmg (a noetic relation) and an 

attempt to get it (any one of the five relations, depending 
upon the kind of object desired) by acting on certain things 
(causal) in such a way that they in turn will do something that 
will lead (causal) to the attainment of the desire. Change 
again, is an alteration (time) in the states (subject and attri- 
bute) or outer relations (causal or non-dynamic) of a thing 
which remains self-identical throughout them all (individual 
identity). This case of Change shows how inextricably dif- 
ferent categories are sometimes interwoven. 

The idea oi whole and part is, as Sigwart points out, primar- 
ily the idea of a relation in space— -/.^., of a larger figure or 
object comprehending or containing a smaller; but in many 
cases the idea involves also the notion of an influence exerted 
by the whole upon the parts or by the parts upon the whole. 
This is most obvious in the case of living beings. It is 
because I can control the movements of my hand and feel its 
injuries that it seems so much a part of me — more so than 
my hair or finger-nails. Thus the idea of whole and part 
often involves both dynamic and non-dynamic relations. 

in the traditional logic, are enumerated near the beginning of the 
"Critique of Pure Reason"; Mill's are given in Bk. I, Chap. V, of his 
"Logic". 

Of all these lists Kant's is much the worst. As to Mill's Existence and 
Non-existence, we shall see in the next chapter that it is not a new kind 
of category comparable with those which I have enumerated ; for as 
Lotze says, " to exist is to stand related ". In other words, ' Existence ' 
is a general term applied to whatever has any of the particular relations 
specified. To exist and to have a place in the world of related things 
are one and the same. 



CERTAIN COMBINED RELATIONS. 85 

The unity of an animal body involves also the relation of 
means and end, since all the parts cooperate. 

The relation of Number corresponds closely with that of 
whole and part. Until a given whole, such as the distance 
from Cleveland to Buffalo, is split up mentally into a series of 
parts each of which is regarded as a whole, we cannot ex- 
press it in numbers, e.g., 61 leagues, 183 miles; until I dis- 
tinguish between the units in ^ a mass of humanity ' (as the 
newspapers sometimes say) or in a flock of sheep or a cloud 
of dust, I cannot count them. The units, of course, can be 
chosen perfectly arbitrarily : leagues, miles, kilometers, per- 
sons, couples, families, dozens, pounds. But they must be 
similar as well as homogeneous ; I cannot add persons and 
miles, and if I wish to add leagues and kilometers I must 
reduce one to the other. Having settled upon our similar 
units, we do not get the idea of any definite number until we 
count them, and this is possible only when they are so 
arranged as to be perceptible separately, that is, only when 
they are a certain distance apart in space, like dots on a 
page or the sides or angles of a figure ; or in time, like suc- 
cessive strokes of a bell or throbs of pain. 

Thus number, like whole and part, is primarily a relation 
of space or time. We can distinguish a triangle from a 
square without counting the sides, because they do not look 
alike. Similarly any single object looks different from 
a group of two or more, and groups of two, three, and 
four look different from each other. Similarly also three 
strokes of a bell sound different from one or two. The 
higher numbers we understand largely through these lower 
ones. To count is thus to tell something about the spatial 
or temporal appearance the objects in question can be made 
to present. 

All propositions are divided by some writers into pure and 
modal. Modal propositions contain some word or phrase to 
intimate " the degree of certainty or probability with w^hich 
a judgment is made and asserted" {e.g.\ Hq ^n\\\ probably 



86 THE RELATIONS EXPRESSED IN PROPOSITIONS. 

come, it will certainly rain, perhaps he is here). Pure prop- 
ositions do not. Of modal propositions we shall have some- 
thing more to say. For the present we may regard the 
modal element as merely noetic, equivalent to some such 
sentence as ' I think so ', ^ I am sure of it ', ^ I am doubtful 
about it ' . 

Some writers v/ho speak of modal propositions include all 
those which contain an adverb, e.g.-. ' He acts clumsily ', ' he 
goes quickly ' . Such adverbs, however, are mere completions 
of the verb, and in many cases they can be avoided altogether 
by using a verb which already contains their meaning, e.g.\ 
' He blunders % ^ he hastens ' . Whether one word or a dozen 
is necessary to tell the precise relations of the object in ques- 
tion is a mere accident of language, and no logical distinction 
should be based upon it. 



CHAPTER VII. 
WHAT PROPOSITIONS IMPLY ABOUT EXISTENCE.* 

When we say that a thing is green or large or terrible, do 
we necessarily imply that it is, or exists ? To put the ques- 
tion in its most general form, does the copula ^ is ' or does 
any proposition imply the existence of the things whose rela- 
tions it affirms or denies? 

In discussing this question it is necessary first of all to dis- 
tinguish between the subject of a relation and what is named 
in the subject of a sentence, for they are not al- r^^^ ^^^ 
ways identical. It is thus possible to believe that ' subjects*, 
every relation involves the existence of something related 
without being forced to conclude that every proposition as- 
sumes the existence of what is named in its subject. By way 
of illustration let us quote some sentences from Keynes : 
^ * The following may be given as examples of universal 
propositions, which need not be regarded as implying the 
existence of their subjects : No unicorns have ever been seen ; 
All candidates arriving five minutes late are fined one shil- 
ling ; Who steals my purse steals trash ; . . . Every body 
not compelled by impressed forces to change its state, con- 
tinues in a state of rest or of uniform motion in a straight 
line. . . . We may make the first of the above assertions 
without intending to imply that unicorns exist unseen ; the 
second does not commit us to the prophecy that any candi- 

* See the excellent chapter in T. N. Keynes' -'Formal Logic", 
Macmillan & Co. 

87 



88 WHAT PROPOSITIONS IMPLY ABOUT EXISTENCE. 

dates will arrive five minutes late ; and similarly for the re- 
maining propositions." * 

The grammatical subjects of these propositions are the terms 
'Unicorn', * Candidates arriving five minutes late', 'He 
who steals my purse ', and ' Every body not compelled by 
impressed forces to change its state', and Keynes is cer- 
tainly right in saying that the propositions in question do 
not imply the existence of any of the things named by these 
terms. 

It is true, nevertheless, that the propositions do imply the 
existence of something ; and this something is the subject of 
the relations expressed. When we say that no unicorns have 
ever been seen we mean that no human being has ever had 
the experience which we call the perception of a unicorn, 
and we take for granted the existence of human beings. The 
statement about candidates arriving late means that if any 
one should appear before a certain board as a candidate but 
should not arrive on time, he would be fined. It assumes the 
existence of the members of the board and of persons who 
may wish to be candidates, and points out certain causal 
relations which may arise between them. lago's words do 
not assume the existence of some one who steals his purse ; 
but they do assume the existence of people who have purses 
and of other people who might steal them if they could. New- 
ton's law of motion does not assume the existence of bodies 
not acted upon from without ; but it does assume the exist- 
ence of material bodies, and helps to explain their nature 
and their movements by telling what any of them would do 
if they were not acted upon from without. 

Thus when we distinguish between the subjects of a rela- 
tion and the things denoted by the subject of a proposition, 
or, better, when we distinguish between the things we are 
really talking about and the things that the structure of a sen- 
tence sometimes makes us seem to be talking about, it is easy 

* Pp. 20I-2, third edition. 



DENIALS OF RELATIONS AND OF EXISTENCE. 89 

enough to see not only that the copula Ms', but that every 
proposition, regardless of the copula, implies the existence 
of that whose relations it discusses. 

The last statement holds true not only of affirmative but 
of negative propositions and even of those in which there is 
a downright denial of existence. 

Negative propositions as such are easily disposed of. When 
we deny that a thing has such and such qualities we usually 
assume that it exists and possesses other qualities Denials of 
incompatible with the first. If any one should ^nd^of^^^ 
assert that John Smith was not good-natured we existence. 
might assume that he was more or less morose. We should 
usually assume that he did exist. Sometimes, however, we 
say that a thing has not certain qualities because it does not 
exist at all ; e.g., ' A snark is not terrible '; ^ ghosts are not 
to be feared'. Here the negative proposition amounts to 
one in which existence is denied. 

But even when we say that something does not exist, our 
statement is really one concerning what does exist. To 
illustrate what I mean let us examine a peculiar but import- 
ant passage in Herbert Spencer's ^^ First Principles" (Pt. 2, 
Cha]). 4). Mr. Spencer thinks that the lately discovered 
law of the conservation of matter is one which no rational 
being ever seriously doubted, even though he supposed him- 
self to do so. He bases this paradox on the conviction 
that nobody can possibly succeed in thinking of nothing. 
Let us see ^^what happens", says Mr. Spencer, '^when 
the attempt is made to annihilate matter in thought. . . . 
Conceive the space before you to be cleared of all bodies 
save one. Now imagine the remaining one not to be re- 
moved from its place, but to lapse into nothing while stand- 
ing in that place. You fail. ... It is impossible to think 
of something becoming nothing, for the same reason that it 
is impossible to think of nothing becoming something — the 
reason, namely, that nothing cannot become an -object of 
consciousness." 



go WHAT PROPOSITIONS IMPLY ABOUT EXISTENCE. 

From this argument about the impossibility of tliinkiiig of 
nothing, Mr. Spencer believes he has proved that no one can 
possibly think of a single atom of matter either beginning or 
ceasing to exist. We must therefore, according to the argu- 
ment, think of the world and every atom in it as eternal, 
uncreated, and indestructible. 

Now, I believe that Mr. Spencer is quite right in saying 
that we cannot think of nothing (a very different thing from 
not thinking at all). Everything w^e imagine or think of 
we tend to think of as existing, and as long as our thought is 
concerned wholly with any given object we cannot possibly 
think, though through force of habit we may perhaps speak, 
of that object as non-existent. But then Mr. Spencer over- 
looked the fact that when we assert a thing's non-existence 
our thought, so far as we have any, is a thought, not of the 
thing, but of the empty background where the thing might 
have been. He is right enough in saying that we cannot im- 
agine a non-existent body as non-existent, but we certainly 
can think, whether we believe it or not, of God existing in a 
worldless void at one instant and with worlds about him at 
the next, or of a universe enriched or impoverished by the ad- 
dition or loss of some speck of dust or of some whole world. 
Certainly every child has seen plants grow without thinking 
of the nourishment they appropriate, and seen them burnt up 
without thinking of the smoke in which their elements are 
preserved. 

The way we think of non-existence is well illustrated in 
the nursery rhyme : 

Old Mother Hubbard 
Went to the cupboard 

To get her poor dog a bone. 
But when she got there 
T/ie cupboard was bare, 

And so the poor dog got none. 

A bare cupboard, a disappointed woman, and a hungry dog ! 
Here is a vivid picture of the bone's absence, but not a v/ord 



THE CONCEPTION OE REALITY. 9 1 

a])Out the bone itself! Our attention is turned not to the 
bone, but to the empty background. ^'As for man, his 
days are as grass ; as a flower of the field, so he flourisheth, 
for the wind passeth over it and it is gone, and the place 
thereof shall know it no 7nore.'" Here again it is the empty 
j)lace, not the grass and the flower, that we must think of in 
order to get the full sense of their annihilation. 

To say that a thing does not exist, means therefore that 
the world or whatever other reality there is exists without it 
and with relations other than those which its presence would 
have involved. 

Thus we think, not of what is not, but of what is ; and 
whatever we think of, we think of as existing in some way or 
other. 

This whole question of existence can be made clear by 

tracing the origin and growth of the distinction between 

realities and illusions or fictions. Young chil- 

, , . T . . ° The con- 

dren cannot make this distinction. Savages ceptionof 

make it very imperfectly, and even adult mem- ^' 

bers of a civilized society often fail in the efl*ort to apply it. 

It sometimes happens that a person hears his name called, 
looks around, can see nobody, and finally concludes that the 
sound was imaginary. At first the sensation of sound car- 
ried with it an instinctive belief in the reality of something 
beyond the hearer which made it. Every sensation does 
this. If it did not we should never be able to perceive 
things at all. Instead of saying, ^ I hear some one speak', ^ T 
see the sun ', ^ I smell a rose ', ^ I feel the ground ', ' There is 
a mouse '; we should only be able to say, ' Lo, a feeling like 
the somid of w^ords !' ' Lo, a vivid sensation of sight !' ^ Lo, 
a sweet smell !' ^ Lo, a touch-feeling !' ^ Lo, a succession of 
peculiar visual and auditory feelings ! ' 

Thus every conception of reality which we have depends 
ultimately upon our instinctive tendency to interpret feelings 
in terms of things acting upon us — to say, not that such and 
such a feeling is now going on, but that such and such an 



92 WHAT PROPOSITIONS IMPLY ABOUT EXISTENCE. 

object is now present. From this tendency to objectify our 
experience we can never wholly escape. 

If when we had sensations we did nothing more than to 
refer them vaguely to something or other acting upon us, we 
should never be able to detect an illusion. As a matter of 
fact we do much more, for we build up as soon as we can the 
conception of a large number of definite objects, acting or 
disposed to act in definite ways upon each other and upon us. 
We learn that sounds and smells come from objects that can 
be seen and handled, and we expect floors to support us, 
food to taste good, and the people around us to be pleased or 
annoyed, as the case may be, at a given kind of conduct. 
We gain, in short, a knowledge of the nature and relations of 
a great many things. Moreover, we expect each thing to 
appear and act at one time as it did under similar circum- 
stances at another. If we did not, there would be no mean- 
ing in the distinction between various kinds of things. 

It is by means of such knowledge of things and the way 
they act that we are able to correct our first impressions and 
distinguish between that which we have experienced and that 
which we have only imagined. If we hear a voice but see 
no one, we conclude that we were mistaken about the voice, 
because it is easier to discredit the testimony of a single sense 
on a few occasions than to discredit our conviction that names 
are not called in the absence of a visible and tangible person 
who calls them. What is true of sensation is true of all 
thought. What we think about, whether it be an ink-bottle 
or a dragon, is thought about, for the instant at least, as 
though it were real, and if we afterwards deny its reality, this 
is because our thought has turned from the object itself to a 
wider system of things in which we find that it has no place. 

We have just seen how we conceive of every object of 
thought as real until we find that it will not fit into a wider 
system of things. The ultimate and highest test of individ- 
ual facts would be, therefore, a thoroughly consistent and 
well-established conception of the whole material and spirit- 



THE CONCEPTION OF REALITY. 93 

ual universe. But this is something which nobody possesses. 
As a matter of fact we seldom think of such a universe at all. 

Knowledge comes at first in disconnected patches. These 
gradually grow together and are combined into larger fields. 
Within each field our conceptions are moderately consis- 
tent, but we rarely think of the relations between various 
fields, or test our conceptions of one by comparing it with 
another. Sunday-school stories, Greek mythology, German 
fairy tales, novels, histories, science, theology: these are all 
more or less consistent within themselves and inconsistent 
with each other. We live as it were at different times in 
different worlds, each dominated by its own fundamental 
laws. We do not expect to find cherubim and archangels 
on Olympus or muses ^'on the secret top of Oreb or of 
Sinai ", nor do we usually think of Hamlet, Solomon, and 
Cinderella meeting together beyond the Styx. As long as 
we keep our worlds apart, each seems real ; the more vividly 
we picture it the more real it seems ; and the impression 
of reality lasts until we compare two inconsistent worlds 
together. I think a good illustration of this is to be found 
in Kipling's story of ^^Mowgli's Brothers". After tell- 
ing how a little naked man -cub toddled into a wolfs den 
and was adopted by Mother Wolf, the author explains what 
Mother and Father Wolf must do in order to have the adop- 
tion legally recognized and ratified by the Pack. 

' ' The Law of the Jungle lays down very clearly that any wolf 
may, when he marries, withdraw from the Pack he belongs 
to ; but as soon as his cubs are old enough to stand on their 
feet he must bring them to the Pack Council, which is gen- 
erally held once a month at full moon, in order that the other 
wolves may identify them. After that inspection the cubs 
are free to run where they please, and until they have killed 
their first buck no excuse is accepted if a grown wolf of the 
Pack kills one of them. The punishment is death w^here the 
murderer can be found, and if you will thiiik for a minute 
you will see that this must be so, " 



94 WHAT PROPOSITIONS IMPLY ABOUT EXISTENCE. 

Now, in the constitution of jungle society as it is pic- 
tured in the story, there is absokitely no reason why 'Hhis 
must be so ", and so when we '' think for a minute " we have 
to seek for the reason in what we know in other ways of wild 
beasts and their habits; and, doing this, we suddenly see the 
gap between the every-day world and the world of Kipling's 
fancy^ and realize how great is the fiction that we have been 
treating as real. 

It is, of course, by our every-day world, the world of 
greatest coherence and most importance for us, that we test 
all others, and for most civilized adults nowadays that world 
is the world of physical and historical science. But it must 
not be forgotten that the scientific conception of the world 
is a very new one. In the middle ages the every-day world, 
the world of greatest coherence and most importance, was 
the world of heaven and hell, God and the devil. Beside 
it the earth and mundane affairs were as visions and empty 
dreams. 

By history we test the truth of stories, but history is of 
more recent origin than physics. It is one great story con- 
sistent with itself and with physical science and comprehend- 
ing and explaining as many shorter stories as possible. Be- 
fore it was told the truth of self-consistent shorter stories or 
sets of stories could not be questioned. Any tale seemed as 
true as any other if it appealed strongly enough to the im- 
agination and emotions of the hearer. It is because they 
know little science and history that children and savages dis- 
tinguish between truth and fiction so imperfectly. 

To ask whether some object really exists or whether some 
story is true implies the possession of some accepted system 
of things by which smaller or less vital systems can be tested. 
If a smaller system is found to agree with the larger a de- 
liberate conviction based upon this agreement is added to 
the spontaneous and na'ive conception of its objects as real. 
The objects are now thought of as real in a new and deeper 
sense. But it must not be forgotten that the distinction 



THE CONCEPTION OF REALITY. 95 

between the two kinds of reality is simply one of degree, and 
that the conception of the reality of the larger system of 
things which we use as a test grows itself out of the same 
spontaneous tendency to objectify our impressions that ac- 
counts for the more fragmentary systems which we have 
tested by means of it. 

When we discuss the nature of centaurs and dragons we 
treat these creatures as real in the sense that we imagine them 
before us with perceptible qualities and relations. We after- 
wards deny their reality in the sense that we seek in vain to 
find a place for them in the wider scheme of consistently re- 
lated things which we have come to regard as alone of vital 
interest. Unless we took the wider system of things for 
granted we could not test the narrower. Thus to deny the 
existence of one thing is really to say something about the 
relations of some wider or more certain universe whose 
existence we assume ; and thus every proposition, whether its 
copula is some part of the verb ' to be ' or whether it is some- 
thing else, implies the existence of something, though not 
necessarily of the object described in its subject. 



CHAPTER VIII. 
THE FORMAL CHARACTERISTICS OF PROPOSITIONS. 

In every proposition something is either asserted or denied 
of a given object more or less definitely pointed out. When 
something is asserted the proposition is called 
and ^ affirmative {e.g., 'Dogs like meat', 'Iron is a 

ft^an y. ix^etal'), when denied, negative {e.g., 'Dogs do 
not like meat ', ' Iron is not a metal '). The character of a 
proposition as affirmative or negative is called its quality. 

When a proposition states something about some one defi- 
nitely designated object it is c2X\i\d. singular , ^-g-, 'Socrates 
was flat-faced ', ' My dog is not savage ', ' The last man in 
the row is my cousin ' . 

When it states something about every member of a desig- 
nated group of objects it is called universal, e.g,, 'All men are 
mortal ^ 'No Spanish-American state has a stable govern- 
ment % ' Every event has a cause '. 

When it states something about some undesignated or im- 
perfectly designated member or members of a given group of 
objects it is called particular, e.g., ' Some of the American 
races were highly civilized', ' One of the men in the row is 
my cousin \ ' Some dogs are not savage ', ' A certain man had 
two sons ' . 

The term ' particular ' is here used in a peculiar sense, 
quite contrary to its ordinary meaning, for particular prop- 
ositions are the only ones which do not give information 
about particular or definitely designated objects. If a gen- 

96 



QUALITY AND QUANTITY. 97 

eral tells his officers that one of them has bhmdered, each 
can ask: Do you mean me ? But if he uses a singular prop- 
osition and says that Captain Jones has bhmdered, or a 
universal and says that they have all blundered, the question 
is no longer possible. The term ^ particular ' as used in logic 
is derived directly from the Latin pariiciila^^ a particle, and 
has been applied to certain propositions merely becciiise, 
unlike universals, they refer to only part of the class or group 
of objects mentioned. 

Singular propositions are usually classified with universals 
because they point out the object spoken of in the same 
definite way, and because for most logical purposes definite- 
ness of reference is much more important than the number 
of objects to which we refer. ^ 

The character of a proposition as universal, singular, or 
particular is called its quayitity. 

If we neglect singular propositions and consider the various 
combinations of quantity and quality in universals and par- 
ticulars there are four kinds of propositions, each of which 
it is customary to denote by one of the following symbols : 

A. Universal affirmative, as ' All S's are P '. 

E. Universal negative, as ' No S is P '. 

I. Particular affirmative, as ^ Some S's are P '. 

O. Particular negative, as ' Some S's are not P \ 

The symbols A and I are respectively the first and the 
second vowels in the word affirvio, E and O belong in the 
same way to nego. 

The reader should notice that the proposition ' All S's are 

* This is the real reason; but it is not always the reason given. 
Whately, for example, says that singular propositions are to be treated 
as universals, because they tell something ' about the whole of the sub- 
ject '. When, for example, we say that Brutus killed Caesar, we are 
speaking about ths whole of Bruttis. . This is of course absurd. We 
should speak just as much about the whole of Brutus if we said that a 
certain Roman killed Caesar. It is not a question of how much ? but of 
who ? or which ? 



9^ FORMAL CHARACTERISTICS OF PROPOSITIONS. 

not P' usually means * It is not true that all S's are P \ i.e., 

^ Not all S's are P ', or ^ Some S"s are not P'. 

of quantity It is therefore O, not E. When we realize that 
or quality. . r ^ ■ i • 

expressions or this sort are ambiguous we 

should try hard to avoid using them. When we find 
them used by others who may not have recognized their 
ambiguity we should try to interpret them according to the 
real meaning of the speaker — if he had a definite meaning 
— and not according to any arbitrary rule. If it is im- 
possible to tell what his real meaning is, we should make 
it plain that this is the case. The one thing that we 
should certainly not do is to allow such expressions to pass 
without question. If we do so they are likely to be taken in 
one sense at one time and in another at another ; and thus 
to lead us to conclusions which wx really have no right to 
reach or to disputes for which there was really no occasion. 

The word ^ few \ as Jevons has pointed out, must be inter- 
preted with care ; ^* for if I say 'few books are at once learned 
and amusing', I may fairly be taken to assert that a few hooks 
certainly are so, but what I really mean to draw attention to 
is my belief that ' the greater nwnher of hooks are not at once 
learned and amusing. ' A proposition of this class is gener- 
ally to be classed rather as O than I ". * 

Whether the word some means some hut not all or at least 
some, perhaps all, depends largely upon the scientific training 
of the speaker. Like the fish that bites at every wriggling ob- 
ject and the baby that grasps everything within its reach re- 
gardless of possible burns or cuts, we all tend to generalize 
too carelessly. When a confiding boy leaves home he is 
likely to take it for granted that every one is trustworthy- 
proposition A ; because of his credulity he is soon cheated, 
and then like David in his wrath he may say that all men 
are liars, i.e,, that no one is trustworthy — proposition E. 
Soon, however, he gets a letter from home or is befriended 

* ''Elementary Lessons in Logic ", p. 67. 



UNDESIGNATED QUANTITY OR QUALrfY. 99 

by an old acquaintance and he qualifies his sweeping con- 
demnation. "Some people are trustworthy", he now says, 
implying that all but a chosen few are unreliable. After a 
while, however, he learns the value of cautious statements, 
and if he should then go to a new place and be fortunate 
in his first acquaintances he might say '^ Some people here 
are trustworthy", implying nothing whatever about the rest 
except, perhaps, that he did not know them. 

In short, the development of particular propositions is a 
mark of increasing caution and accuracy. The end which 
they serve is therefore defeated, at least in part, when they 
are understood to imply more than they state. Often they 
do imply more — but merely because a speaker or hearer is 
not yet sufficiently w^ell trained to realize that a qualified 
statement can be made on general principles. Here again 
one must take care to speak in such a way as to be under- 
stood aright by his hearers (whoever they may be), and to 
try and find a definite interpretation for the statements of 
others which they themselves would accept. 

Instead of being ambiguous, words used to denote quan- 
tity and quality are often lacking altogether. Undesignated 
Sometimes the meaning is clear enough without Quantity or 
them; but sometimes it is not. 

The term indefinite, indesignate, or preindesignaie is applied 
to propositions whose form does not show whether they are 
intended to be universals or particulars. When, for exam- 
ple, we say that dogs delight to bark and bite, or that 
republics are more free than monarchies, or that crows are 
black, do we mean the statement to apply to every dog, 
every republic, every crow, or only to some larger or smaller 
number of them .? Indefinite propositions must not be con- 
fused with particulars. The quantity of a particular proposi- 
tion is perfectly clear, but the object to which it refers is not 
definitely designated. The quantity of an indefinite proposi- 
tion, on the other hand, is not clear, and for that reason it 
is impossible to say whether it is meant to refer to any 

Lore. 



100 FORMAL CHARACTERISTICS OF PROPOSITIONS. 

definitely designated objects or not. Particular propositions 
are indefinite in their reference; indefinite propositions, 
ambiguous. 

When the form of a proposition gives no indication of its 
quantity it is very easy to accept it or prove it true when 
interpreted as a particular and then use it as though it were 
true as a universal. Here is an example: "Improbable 
events happen almost every day; events which happen almost 
every day are probable events; therefore improbable events 
are probable events.'' When the first premise of this 
argument is assumed to be true it is evidently understood 
to mean that some improbable event or other happens almost 
every day; and from it in conjunction with the other 
premise we have the right to conclude that the occurrence 
of some improbable event or other is probable, but nothing 
more. When the premise is understood in this sense 
throughout it certainly will not help us to conclude that 
improbable events are probable events. It is capable, how- 
ever, of being interpreted to mean that every improbable 
event happens almost every day; and when taken in this 
latter sense it certainly will help us to reach the conclusion. 
Every improbable event happens almost every day; events 
which happen almost every day are probable events; there- 
fore every improbable event is a probable event. But, then, 
when the premise is understood in this sense nobody would 
admit its truth. 

We must not assume, however, that the quantity or qual- 
ity of a proposition has not been indicated merely because it 
has not been expressed formally by one of the words ' some ', 
' all \ ' none', ' not '. Minto puts the matter as follows: 

"The expression of Quantity, that is, of universality or 
non-universality, is all-important in syllogistic formulae. In 
them universality is expressed by all or none. In ordinary 
speech universality is expressed in various forms, concrete 
and abstract, plain and figurative, without the use of ' all ' 
or ' none '. 






UNDESIGNATED QUANTITY OR QUALITY. loi 

Uneasy lies the head that wears a crown. 

He can't be wrong whose life is in the right. 

What cat's averse to fish ? 

Can the leopard change his spots ? 

The longest road has an end. 

Suspicion ever haunts the guilty mind. 

Irresolution is always a sign of weakness. 

Treason never prospers. 

* * ^ * * ^ 

"All the above propositions are ' Pre-designate ' [i.e., 
definite] universals, and reducible to the form All S is P, or 
No S is P. 

"The following propositions are no less definitely par- 
ticular, reducible to the form I or O [i.e., Some S is P, or 
Some S is not P]. In them, as in the preceding, quantity 
is formally expressed, though the forms used are not the 
artificial syllogistic forms: 

Afflictions are often salutary. 
Not every advice is a safe one. 
All that glitters is not gold. 
Rivers generally run into the sea. 

" Often, however, it is really uncertain from the form of 
common speech whether it is intended to express a universal 
or a particular. The quantity is not formally expressed. 
This is especially the case with proverbs and loose floating 
sayings of a general tendency. For example : 

Haste makes waste. 

Knowledge is power. 

Light come, light go. 

Left-handed men are awkward antagonists. 

Veteran soldiers are the steadiest in fight. 

" Such sayings are in actual speech for the most part 
delivered as universals. It is a useful exercise of the Socratic 
kind to decide whether they are really so. This can only 



I02 FORMAL CHARACTERISTICS OF PROPOSITIONS. 

be determined by a survey of facts. The best method of 
conducting such a survey is probably (i) to pick out the 
concrete subject, ' hasty actions ', ' men possessed of knowl- 
edge ', * things lightly acquired ' ; (2) to fix the attribute or 
attributes predicated; (3) to run over the individuals of the 
subject class and settle whether the attribute is as a matter 
of fact meant to be predicated of each and every one. 

" This is the operation of Induction. If one individual 
can be found of whom the attribute is not meant to be 
predicated, the proposition is not intended as universal. 

** Mark the difference between settling what is intended 
and settling what is true. . . . 

"The bare forms of Syllogistic are a useless item of 
knowledge, unless they are applied to concrete thought. 
And determining the quantity of a common aphorism or 
saw, the limits within which it is meant to hold good, is a 
valuable discipline in exactness of understanding.'' * 

When the function of a proposition is, not to describe 
some one object or set of objects, but to tell of a causal or 
Double other relation which exists between several {e.g., 

quantity. John strikes James; David defeated the Philis- 
tines), it is rather arbitrary to determine the quantity of the 
proposition with reference merely to what happens to be 
named in the subject. It would be fairer to recognize both 
parties to the relation, and to determine the quantity of the 
proposition with reference to each. ' Each of these hunters 
shot a bird ' is a universal proposition with reference to the 
hunters, but particular with reference to the birds. ' Almost 
any Turk hates a Greek ' is particular with reference to the 
Turks, universal with reference to the Greeks. * All Turks 
and Greeks hate each other ' is universal with reference to 
both. ' There are many thieves in the land ' is particular 
with reference to the thieves, singular with reference to the 
land. 

* William Minto, ''Logic, Inductive and Deductive *\ Scribners, 
1895. PP- 70-73- 



EXCLUSIVES AND EXCEPTIVES. 1 03 

Let it be remembered, therefore, that though it may 
sometimes be convenient to describe the quantity of such a 
proposition with reference to only one of the related parties 
such a description is both arbitrary and incomplete. 

There are two closely allied kinds of propositions, much 
harder to define than to deal with in practice, called respec- 
tively exceptive and exclusive. The subiect of 

/ , . T T , . . . / Exclusives 

each kind contams some such limitmg phrase as and 

none but, only, alone, except ; and on this account 

they are often confused, in spite of a real contrast between 

them. 

Exceptive propositions state that something is true of all 
the members of a given group of objects except those speci- 
fied. Exclusive propositions, on the other hand, state that 
something is true of certain specified members of a group 
only. 

Here are some examples of the two: 

Exceptive affirmative: All but the Germans departed. 
Exclusive " : The Germans alone departed. 

Exceptive negative: No one but the Germans departed. 
Exclusive " : The Germans alone did not depart. 

Exceptive affirmative : All but the brave deserve the fair. 
Exclusive " : The brave alone deserve the fair. 

Exceptive negative : None but the brave deserve the fair. 
Exclusive " : The brave are the only ones who do 

not deserve the fair. 

It will be noticed that each kind of proposition can be 
either affirmative or negative,* and that the exclusive affir- 

* The fact that each kind of proposition can be either affirmative or 
negative is overlooked in some of the text-books. Jevons, for example, 
assumes in the following definitions that both kinds must be affirmative: 
'< Exceptive propositions affirm a predicate of all the subject with the 
exception of certain defined cases, to which, as is implied, the predicate 
does not belong.'* ''Exclusive propositions contain some words, such as 
only^ alone^ none btit, which limit the predicate to the subject." Where 
a predicate is ' limited to a subject ', it is certainly affirmed and not 



104 FORMAL CHARACTERISTICS OF PROPOSITIONS. 

mative has the same meaning as the exceptive negative, and 
vice versa. 

In the first set of examples above given there can be no 
doubt about the meaning: in each case we are told that the 
Germans did one thing and that the others did the other. 
In the second set, however, the meaning is not so clear. 
When we say that all but the brave deserve the fair, or, to 
make the example less unnatural, all but the brave deserve 
to die, or that the brave are the only ones who do not 
deserve to die, do we mean that every brave man deserves 
to live, or merely that so far as courage is concerned, brave 
men do not deserve death .? In the latter case a brave man 
might deserve it on other grounds. So when we say that 

denied of the subject. Both definitions thus assume that the propositions 
are affirmative. As examples of exclusive propositions Jevons gives 
''Elements alone are metals" and ''None but elements are metals". 
He states that they are equivalent and assumes that they are both 
affirmative. As an example of exceptive propositions he gives "All the 
planets except Venus and Mercury are beyond the earth's orbit ". But 
suppose that instead of affirming this we should deny all the facts as- 
serted, the proposition would then read : None of the planets except 
Venus and Mercury are beyond the earth's orbit. This form is pre- 
cisely identical with " None but elements are metals", which Jevons 
regards as an affirmative exclusive proposition. The form is clearly ex- 
ceptive and clearly negative, and there is no reason why the proposi- 
tion should be regarded as either exclusive or affirmative, unless the 
distinction between the two kinds of proposition is abolished altogether. 
This is actually done by Minto, as follows : " The formula for Exclusive 
Propositions. ' None but the brave deserve the fair ' ; ' No admittance 
except on business ' ; ' Only Protestants can sit on the throne of Eng- 
land '. These propositions exemplify different ways in common speech 
of naming a subject exclusively^ the predication being made of all outside 
a certain term." (P. 76.) The trouble with this description is that 
where the subject is 'named exclusively', as in the example about 
Protestants, the predication as it stands is not made about ' all outside 
the term ', but about those inside it. On the other hand, when the 
predication is made about ' all outside the term ' as in the two other ex- 
amples, the subject is not ' named exclusively ' ; for that which is named 
is not the subject. 



EXCLUSIVES AND EXCEPTIVES. I05 

the brave alone deserve the fair or that none but the brave 
deserve the fair, do we mean that every brave man deserves 
a fair wife no matter what he may be in other respects, or 
merely that to deserve one he must at least be brave ? 

The first set of propositions are unambiguous because they 
are purely historical statements about certain individuals as 
such. The second are ambiguous because they express 
conditions about kinds of objects and they do not make it 
plain whether the condition mentioned is or is not the only 
one upon which the case depends."^ 

■^ Exclusive and exceptive propositions can be varied a good deal in 
quantity. When we say The Germans alone remained we (i) specify 
clearly the smaller group (of Germans as distinguished from the rest of 
the persons involved, and {2a) say something about each member of the 
specified smaller group (they remained) and (2d) about each of the rest 
(they did not remain). The proposition is thus in every possible respect 
universal. 

When we say The brave alone deserve the fair, we (i) distinguish 
clearly enough between our groups, [2d) we say something about all 
who are not brave, and {2a) if we are interpreted as saying anything 
at all about those who are brave, — namely, that they li a ve complied with 
one condition — we say it about all of them. This proposition is thus 
also universal in every respect. 

When we say Some of the Germans were the only persons who re- 
mained, we still (i) specify the smaller group clearly and [2d) still say 
something about all the persons outside of it ; but {2a) the individuals 
within it of whom we speak are no longer definitely designated. The 
proposition is thus in one respect particular. When we say The Ger- 
mans and some others alone remained, i is still definite, 2a is universal, 
and 2d particular. When we say Some of the Germans and some of 
the others alone remained, the groups are still clearly distinguished, but 
the original proposition is broken up into two exclusives, each particular 
in so far as it fails to specify the distinction between those who did and 
those who did not stay. Each of these exclusives is equivalent to both 
I and O : some stayed and some did not. 

When we say The soldiers of one nation alone remained, a statement 
is made (2) about each member of each group. To this extent the 
proposition is universal. But as (l) the smaller group is no longer defi- 
nitely specified, the proposition is in this respect particular. 

The precise meaning as to quantity of an exclusive or exceptive 
proposition, like that of any other, may be indefinite. 



lo6 FORMAL CHARACTERISTICS OF PROPOSITIONS. 

So far we have been dealing with what are called categori- 
cal propositions; those in which something is, or at least 

seems from the form of the proposition to be, 
Disjunctives ^ - ^ -, ^ • ^ 

and Hypo- Stated without alternative and without condi- 
tion. Propositions in which it is affirmed that 
one or other of several alternative states of affairs exists are 
called disjunctive or alternative, e.g., Every man is either 
married or single; He is either a fool or a knave; Either he 
is a knave or I have been grossly deceived; Either A or B 
did it; He is either not here or not there.* Propositions in 
which it is affirmed that if some specified state of affairs 
exists another specified state of affairs also exists are called 
hypothetical ^\ e.g., If he is not a fool he is a knave; If he is 
a knave I have been grossly deceived; If he is not in the 
room he is not in the house. 

The part of a hypothetical proposition which specifies the 
condition, either of something being so, or of our knowing 
it, is called the antecedent, the part which specifies what 
follows from that condition is called the co?tsequent. 

Disjunctive propositions state that one of two things must 
be true; but do they imply that both cannot be true .? This 
question has been discussed at much length. If a man is 
married he cannot possibly be single. We know this from 
the nature of things, but there is no reason in the nature of 

* A negative proposition asserts the existence of a state of affairs just 
as much as an affirmative. 

•^ " This is the familiar form of the disjunctive judgment. ... It is 
usual to mention along with it the coputative judgment (' S is both p 
and q and r '), and the re??iotive judgment (' S is neither p nor q nor r *); 
but in spite of the external analogy of form, neither of these has the 
same logical value as the disjunctive ; the first is only a collection of 
positive, the second of negative, judgments with the same subject and 
different predicates, which latter are not placed in any logically im- 
portant relation to each other. The disjunctive judgment alone ex- 
presses a special relation between its members : it gives its subject no 
predicate at all, but prescribes to it the alternative between a definite 
number of different predicates.'* Lotze, ''Logic", § 69. (Clarendon 
Press.) 



DISJUNCTIVES AND HYPOTHETICALS. 107 

things v/hy a person cannot be both fool and knave. When 
it is asserted that he is either one or the other, is it neces- 
sarily implied by the form of the statement that he is not 
both ? Fowler says: '' It seems to me that in the expression 
* either — or — ' we distinctly exclude the possibility of 
both alternatives being true, as well as of both being false. 
In fact, when we do not wish to exclude the possibility of 
both being true, we add the words ' or both ', thus: ' He is 
either a fool or a knave, or both ' ; ' 1 shall come either 
to-day or to-morrrow, or perhaps both days'.'' * With this 
view Thomas Aquinas, Kant, Hamilton, Boole, Bradley, 
and others agree. Whately, Mansel, Mill, Jevons, Keynes, f 
and others maintain on the other hand that such proposi- 
tions merely mean that both alternatives cannot be false, 
though both may be true. Says Keynes: " Suppose it laid 
down as a condition of eligibility for some appointment that 
every candidate must be a member either of the University 
of Oxford, or of the University of Cambridge, or of the 
University of London. Would any one regard this as imply- 
ing the ineligibility of persons who happened to be members 
of more than one of these universities ? " 

The question is, of course, one of the interpretation of 
language, not of logical processes. So far as logic is con- 
cerned any one is at liberty to use language in any sense he 
pleases, provided that he explains beforehand the sense in 
which he means to use it; but since there is a real difference 
in usage it seems to me better in this case, as in the case of 
the word ' some ', to assume that the words are used with the 
greatest caution and imply nothing but what is stated. Let 
us, therefore, agree, at least for the purposes of this book, 
that when we say that one or other of several alternatives is 
true we do not necessarily imply that both cannot be true, 
though of course we do imply that both cannot be false. 

* '< Deductive Logic ", p. 118, Ninth Ed. (Clarendon Press), 
j- See Jevons, ''Principles of Science ", p. 68, and Keynes, *• Formal 
Lo^ic ", § 140, 



io8 FORMAL CHARACTERISTICS OF PROPOSITIONS. 

Like exclusive and exceptive propositions, hypothetical 
and disjunctive propositions are different in form and must 
be distinguished from each other, though they can be made 
to express the same meaning. The following table shows 
the relations between them: 

Disjunctive. Hypothetical. 

A is either B or C = If A is not E, it is C. 

= If A is not C, it is B. 
A is either not B or not C ~ If A is B, it is not C. 

— If A is C, it is not B. 
A is either B or not C = If A is not B, it is not C. 

= If A is C, it is B. 

In each case there are two hypothetical propositions, 
either of which is equivalent to the disjunctive, and each of 
which is exactly equivalent to the other. To say If A is not 
B it is C means precisely the same thing as to say If A is not 
C it is B; and so with the rest. 

If any one were asked the use of disjunctive and hypo- 
thetical propositions, the first answer that occurred to him 
would probably be: To express knowledge combined with 
doubt. To use Venn's illustration, if I say that A.B. is 
either a barrister or a solicitor, I express my knowledge that 
he is a lawyer and my doubt as to his precise standing at 
the bar. The same thought would be expressed in the 
hypothetical proposition, ' If he is not a barrister he is a 
solicitor '. 

But disjunctive and hypothetical propositions are not 
always used to express doubt. When, for example, we say 
that in the United States every person is either married or 
single, the statement does not express the slightest doubt as 
to the condition of any given individual in this respect. Its 
real force is to explain the laws or social customs of the 
country, under which a person is regarded as single until 
some prescribed condition has been fulfilled, and then as 
married. The statement would hardly hold of an oriental 



DISJUNCTIVES AND HYPOTHETIC ALS. 109 

society in which concubinage was recognized. Such propo- 
sitions, therefore, express knowledge, not ignorance; but it 
is a knowledge of the laws or general conditions of existence 
prevailing in any sphere or ' universe ', not of the precise 
state of some particular individual in that universe. 

In the example just discussed the proposition affirming 
the existence of a general law happened to be disjunctive. 
It is more common to affirm such laws in hypothetical, or 
even in universal categorical propositions^ ^-g-y If a man is 
insulted he becomes angry, or Insulted men become angry; 
When it rains hard the streets are wet, or Hard rains wet 
the streets; The nearer bodies get together the more they 
attract each other, or Contiguous bodies attract each other 
more than those that are farther apart. "^ 

* On p. 87 there are examples taken from Keynes of several other 
universal propositions of this kind. Such propositions, as we there saw, 
do not necessarily imply the existence of things as they are described in 
the grammatical subjects of the propositions ; but they do imply the 
existence of a universe whose laws they more or less accurately express. 
There doubtless are universal propositions founded upon direct observa- 
tion of the things named in them and intended to imply the existence of 
those things as well as to describe them ; e.g., None of the Stuarts 
were good sovereigns ; Each of the United States contains colored citi- 
zens. Such propositions cannot be put into hypothetical form. But 
universals arrived at by deductive reasoning, or reasoning from general 
considerations, are probably always capable of being put into hypo- 
thetical form and seldom or never necessarily imply the existence of the 
things described by their subjects, though they probably do imply the 
existence of the things named in the equivalent hypothetical proposi- 
tions, e.g., Seniors are wiser than Sophomores ; Every husband has a 
wife. Turned into hypothetical form these propositions would run : If 
a person belongs to the Senior class he is wiser than if he belonged only 
to the Sophomore class. If a man is married, he has a wife. The 
general consideration in the first of these examples lies in the supposed 
law of the college universe, that two more years of college life must add 
something to one's wisdom.. It is a statement which will be as valid 
as it is now as long as colleges and human nature remain what they 
are. It is not concerned specially with the present, the past, or the 
future existence of Seniors and Sophomores and colleges, the present 
term of the verb to he, like the phrase must de, being used in a perfectly 



Tio FORMAL CHARACTERISTICS OF PROPOSITIONS. 

timeless sense. The proposition merely states the effects supposed to 
result from certain causal agencies whenever and wherever they may be 
supposed to exist. The statement that every husband has a wife is 
based upon a similar consideration of the nature of things. We mean 
by a husband a man who is married, and we know perfectly well that as 
the world is constituted men can marry only women, that is, wives. It is 
this general fact which the proposition expresses; it does not necessarily 
imply that any one is married. 

Particular propositions, unlike universals, are not usually deduced 
from general considerations ; though sometimes they may be : e.g.^ 
*■ Some Sophomores uiust be wiser than the average Senior '. As a 
rule, however, particular propositions are based upon the direct obser- 
vation of individuals to which we are forced to resort when general con- 
siderations are inapplicable, and they naturally imply the existence of the 
individuals observed. The propositions Some Sophomores are wiser 
than some Seniors, Some husbands are not happy, do not lay down 
general laws of the universe or state the effects that certain causes nec- 
essarily produce. For this reason they would hardly ever be put into 
disjunctive form, for though such a form is possible in this case it is 
not very clear, and has no special value when the implication of general 
law is omitted ; e.g.^ A student either is not a Sophomore or is a mem- 
ber of a group of persons some of whom are wiser than some Seniors. 
Put into hypothetical form particular propositions have considerable 
significance, for they serve to deny the existence of the kind of law that 
universals of opposite quality assert ; e.g.^ If a person is a Sophomore he 
may be wiser than a Senior. This is the hypothetical form of the par- 
ticular proposition ' Some Sophomores are wiser than some Seniors '. 
They both serve to deny the universal law expressed in the universal 
categorical proposition, • No Sophomore is wiser than a Senior ', or in 
the hypothetical proposition, ' If a student is a Sophomore he is not as 
wise as a Senior'. 

Universal laws expressible in the above forms can also be expressed 
by the phrases ??mst be, are necessarily, etc., and denied by the phrases 
need not be, are not necessarily, etc. 



CHAPTER IX. 
THE OPPOSITION OF PROPOSITIONS. 

In the last two chapters we dealt with the deeper inter- 
pretation of propositions. We must now discuss another 
question which is practically one of interpretation, but 
which is not at all deep. Such a discussion is important 
enough to be found in all the text-books of logic; and yet 
the only end which it serves is to force the reader to think 
about the obvious meaning of his words and to show him 
how easy it is to make foolish blunders when we rattle off 
words without thinking. 

The ' Opposition of Propositions', as the phrase is used 
in logic, means merely the mutual implications of proposi- 
tions which differ in quantity or quality or both. To be 
' opposed ' in this sense it is therefore not necessary that 
two propositions should be inconsistent. This use of the 
term opposition is not happy, but since it is common we 
must understand it. 

Anybody who will exercise a little patience ought to be 

able to work out an answer to this question : Assuming the 

truth or the falsity of one of the propositions A, With com- 
T^ T 1 /^ 1 1 11 1 ^on propo- 

iL, I, and O, what can we know about the truth sitions. 

or falsity of the others ? If it is true that all the members of 

the present senior class are in good health (proposition A), 

is it true or false that some of them are in good health 

(proposition I), that none of them are in good health 

(proposition E), that some of them are not in good health 

(proposition O) ? 

For the sake of helping the reader to verify his reasoning 

I shall give a table showing the relations of the various cate- 

III 



I r 2 



THE OPPOSITION OF PROPOSITIONS. 



gorical propositions. This table, like any other that may be 
found in a text-book of logic, ought to be understood, but 
not learned by heart. The only thing in logic that ever 
ought to be learned by heart is a definition, for we must 
depend upon memory for a precise meaning of words, but 
even a definition ought not to be learned in this way, if 
there is any other way in which a person can remember and 
restate its precise meaning. With a logical table the case 
is entirely different. It is valuable only because clear think- 
ing is required to construct it. It is not worth remember- 
ing; and to commit it to heart like a multiplication table is 
a pure waste of time. 



If A is true, 


E is false. 


I true. 


false. 


'' E '^ '^ 


A " false. 


I false. 


true. 


<< J 11 ii 


A '' doubtful. 


E false, 


doubtful. 


<< Q ii a 


A " false. 


E doubtful, 


I doubtful. 


*' A is false, 


E is doubtful, 


I doubtful, 


true. 


'' E '' " 


A '' doubtful. 


I true. 


doubtful. 


«' J ii a 


A '' false. 


E true, 


true. 


*' Q ii ii 


A " true. 


E false, 


I true. 



This table is concerned only with the relations of universal 
propositions and particulars. It tells us nothing about the 
relation of either universals or particulars to propositions 
which tell something about some designated individual or 
class of individuals within the larger group. If we designate 
all propositions dealing with a designated individual or class 
within the larger group by the letter S we get the followng: 

If A is true, S affirmative is true and S negative is false. 



E " " S 


" false 


S 


i i 


" true. 


I " " S 


"doubtful" 


s 


i i 


" doubtful. 


" " s 


"doubtful" 


s 


i i 


" doubtful. 


A is false, S ' 


"doubtful" 


s 


i i 


" doubtful. 


E" " S 


"doubtful" 


s 


i i 


" doubtful. 


I " " S 


" false 


s 


i i 


" true. 


0" " S 


" true 


s 


i i 


" false. 



WITH COMMON PROPOSITIONS. 1 13 

If S aff. is true, A is doubtful, E false, I true, O doubtful. 
If S neg. is true, A is false, E doubtful, I doubtful, O true.* 

It should be noticed that the truth of a universal proposi- 
tion involves the truth of the corresponding singulars and 
particulars, and the falsity of a singular or particular involves 
the falsity of the corresponding universal, but not vice versa. 

Of propositions which differ only in quality, if both are 
particular one must be true and both may be; if both are 
universal one must be false and both may be. Of the 
propositions A, E, I, O, having the same subject and 
predicate, it is only when they differ in both quantity and 
quality {i,e,, A and O, E and I), that one must necessarily 
be true and the other false. Such propositions are called 
contradictories. Universal propositions of different quality 
(/. ^. , A and E), are called contraries. 

To ' contradict ' a statement is to deny its truth. If you 
make any statement whatever (e.g., that the moon is made 
of green cheese, that every Englishman likes roast beef), and 
if I say ' Ehat is not true ', I contradict you, and the impor- 
tant thing to notice is that if either of us is right the other 
is wrong, and, vice versa, if either of us is wrong the other is 
right. We cannot both be right, and we cannot both be 
wrong. To contradict a statement it is not necessary to 
say ' That is not true ' in these exact words. Any statement 
contradicts another if the two are so related that when either 
of them is true the other must be false and vice versa. In 
formal logic, however, contradictory propositions are sup- 
posed also to have the same terms in the subject and in the 
predicate, thus : ' The moon is made of green cheese ' and 
* The moon is not made of green cheese ', ' All Englishmen 
like roast beef ' and ' Some Englishmen do not like roast 
beef \ In connection with this last example it must be 

* It is often said that for logical purposes singular propositions can be 
treated as universals. In the present case they must be treated rather as 
particulars, though not precisely. In actual experience the matter pre- 
sents no difficulties, 



114 



THE OPPOSITION OF PROPOSITIONS. 



noticed that the contradictory of a universal proposition is 
always either a particular or a singular, and that of a par- 
ticular a universal. Universal propositions of opposite 
quality (' All Englishmen Hke roast beef \ ' No Englishmen 
like roast beef') cannot be contradictories; for while they 
cannot possibly both be true, they may both be false. Such 
propositions are always ' Contraries '. 

The lesson to be learned from these facts is that guarded 
statements are often quite as useful as sweeping statements 
and much safer. If two opponents make guarded state- 
ments both may be right; if they make sweeping statements 
they cannot both be right, but both may be wrong; and if 
either of them makes a sweeping statement, the other need 
not make a statement equally sweeping in order to prove 
him wrong, for a universal proposition can be disproved by 
a single exception. Cautious statements may not always be 
very interesting, but they are not likely to be ridiculous. 

The terms contrary and contradictory are the only ones 
in this connection which for ordinary purposes are worth 
remembering. There are others, however, whose meaning 
is made clear enough in the following traditional * square 
of opposition ' : 



Contraries 



r—i 



n 



..s> 



% 



.^ 






,0° 



>^ 



xS^v 



•Subcontraries- 



'M 



r-t-" 

CD 

CO 



..o 



A and E are each called a subalternans (active). 
I and O are each called a subalternate (passive).* 

*The table which I have given on p. 112 (not the square) shows the 
relations of the various propositions wh'^in it is taken for granted that 
objects of the kiiid described in their subjects exist. We never talk 



WITH EXCLUSIVES AND EXCEPTIVES. tl5 

What the logical opposites of exclusive and exceptive 

propositions are depends upon their interpretation. We 

have seen that when propositions in this form 

relate concrete tacts about individual objects sivesand 

cxccDtivcs 
they usually imply something about the objects 

specifically mentioned as well as about the other members 

of the class in question, but that when they express some 

about things that we do not assume for the moment at least to exist in 
some universe or other. But when a universal proposition is used as 
the equivalent of a hypothetical to express a general law, then the thing 
as it is described in the subject of the universal categorical proposition is 
not what we are really talking about and the proposition does not neces- 
sarily imply its existence. This has been already explained. (See p. 87.) 
It has also been pointed out that particular propositions usually do imply 
the existence of things as they are described in the subject. Particular 
propositions therefore imply something that one kind of universal prop- 
ositions do not imply. In this case therefore the truth of the universal 
does not necessarily imply the truth of the particular. By way of exam- 
ple let us suppose that the universal proposition ' Candidates arriving 
late are fined ' is equivalent to the hypothetical ' If any candidate 
arrives late he will be fined'. This statement may be true as stating a 
rule of the board whether any candidate happens to be late or not. But 
if the particular proposition ' Some candidates, or some of the candi- 
dates, arriving late are fined ' means that there are candidates arriving 
late and some of them are fined; then this statement is not true unless 
there are candidates arriving late. It may thus be possible that the 
universal proposition is true when the particular is false. 

Similarly if particular propositions imply the existence of candidates 
arriving late and there are not any, the propositions I and O will both 
be false at the same time, as they cannot be when the existence of the 
objects named is taken for granted throughout. 

Keynes thinks that it can be shown in a similar way that ** the ordi- 
nary doctrine of contrariety does not hold good ". If universal propo- 
sitions do not imply the existence of the kind of things described in their 
subjects, ^'- All S is P and 720 S is i^are not inconsistent with one another, 
but the force of asserting both of them is to deny that there are any S's ". 
(p. 195.) To take his example, if there is no such thing as an honest 
miller it is true that an honest miller has a golden thumb, and it is true 
that he has not. 

I tllink that here Dr. Keynes is mistaken. The statement that an 
honest miller has a golden thumb is equivalent to the hypothetical: 'If 



Il6 THE OPPOSITION OF PROPOSITIONS. 

general law or condition it is only the unspecified members 
of the class about which something is necessarily implied. 
* Only the red pills are to be taken ' means that the red pills 
are to be taken, and the others left; ' Only the good are 
happy ' means that goodness is essential to happiness, so 
that the bad are never happy; but it does not mean that 
every good man is happy. 

To take the last case first; apart from the implication of 
a general law which may be contradicted by saying that 
virtue is not at all essential to happiness, the proposition is 
merely equivalent to the statement that no bad people are 
happy, or that all happy people are good; and the logical 
opposites of these propositions are obvious. 

In the other case (Only the red pills are to be taken), 
where an exceptive or exclusive proposition is equivalent to 
two ordinary propositions (The red are to be taken and the 
others are not to be taken), it would be false if any of the 
following were true : 

a miller is honest his thumb turns into gold *. Of course this is intended 
to imply that honest millers are not to be found, but it also implies the 
existence of some occult causal relation between honesty in a miller and 
a golden thumb, and a person cannot deny the statement without imply- 
ing that this conception of the universe is fictitious. 

On the whole subject see Keynes, pp. 186-210. 

Since hypothetical propositions and universals equivalent to them are 
usually intended to imply the existence of some general law, they are 
sufficiently contradicted by any proposition denying the existence of such 
a law. The equivalent statements ' If a man is rich he is stingy ' and 
' All rich men are stingy' can be ahvays contradicted by the statement 
'■ It is not always so '; but if the supposed causal relation between riches 
and stinginess were the real subject of interest it would be sufficient to 
say ' It is not necessarily so ' ; and this might be proved even though no 
concrete exception to the universal categorical proposition could be found. 
To put the matter otherwise: Hypothetical propositions tell what under 
certain circumstances fnnst be. To contradict them it is sufficient to say 
that it 7ieed not be. This can be proved by slewing that it sometimes 
is not^ but if a concrete exception could not be found it might be proved 
in some other way. 



SYMBOLS. 117 

(i) Neither the red are to be taken nor the others not to 
be taken = The others alone are to be taken. 

(2) The red or some of the red are not to be taken. 

(3) The others or some of them are to be taken. 

(4) Either the red or some of them are not to be taken 
or the others or some of them are to be taken. 

The last of these four propositions — the disjunctive — is 
the onlv one that must necessarily be true when the oris^inal 
proposition is false. It therefor^i is its contradictory. The 
first of the four is the most extreme statement in the other 
direction. It therefore is the contrary of the original. The 
other two are contraries or c-jutradictories of the parts mto 
which the original is resolved. 

From all this it can be seen that a logical opposite of an 
exclusive or exceptive proposition is itself rarely exclusive 
or exceptive. 

To give concreteness to what has been said about the 

opposition of propositions the followins: svstem 

Y . . . ^ "^ . "" ' Symbols, 

of symbols is suggested. 

Let a small circle represent any object S of the kind dis- 
cussed, and a plain stroke through it ci) indicate the presence 
of a given attribute P, while a stroke with a small bar or 
tick across it ® indicates the absence of that attribute. It 
IS evident that the stroke cannot be both plain and 
crossed. 

Suppose all the objects of the kind discussed to be repre- 
sented by a number of small circles. When anything is said 
about all the objects of the kind under discussion draw a 
plain or ticked stroke as the case may be through each of 
the little circles. When something is said about only some 
of the objects leave some of the circles unmarked. The 
result IS as follows : 

A: All S IS P 9 9 Cj) 

E: No S is P 6*6 

I : Some S is P (() (j) o 

O : Some S is not P ©06 



Ii8 THE OPPOSITION OF PROPOSITIONS. 

I and O : Some S is P and some is not (]) (j) ^ ^ o 

T.o show how these symbols help. Let us represent the 
supposed fact that All S is P — that every circle has a plain 
stroke through it — thus: (|) (j) (|) (|) It does not matter 
how many of these circles we draw so long as the plain stroke 
is drawn through each one of them, to show that there are 
no exceptions. 

Now suppose the question to arise: How many of these 
S's have a crossed stroke } We need only glance at the 
circles to see that there are none marked that way and no 
unmarked circles that might be marked that way. Hence 
we say: None of the circles can be marked with a crossed 
stroke; none of the S's can be non-P; no S is non-P. Thus 
the symbols enable us to see that this follows from the sup- 
posed fact that each of the S's is P. In the same way if each 
of the S's is P — if each circle has a plain stroke — we need 
only look at the above figures to see that it is also true that 
at least some of the circles have plain strokes — that some 
S's are P (Proposition I); false that some of the circles have 
not plain strokes — that some S's are not P (Proposition O); 
and still more false that none of the circles have plain strokes 
— that no S's are P (Proposition E). 

Again, let us suppose that some S's are not P (Proposition 
O) and represent it by drawing a crossed stroke through 
some but not all of the circles — it does not matter how 
many: ^ ^ o o We leave some of the circles unmarked 
because there are some that the proposition does not say 
anything about. We know that in reality each of these 
must have one character or the other, but we do not attempt 
to represent it until we know which character it is. 

What now can we say about the truth or falsity of the 
statement that no S's are P (Proposition E) — that none of 
the circles should really be marked with a plain stroke .? 
All we can say is that the marks already there will not tell 
us. In other words, if we know that Proposition O is true 



SYMBOLS. 119 

and if that is all we know, we must remain in doubt about the 
truth or falsity of E. So likewise with I; so long as we do 
not know whether those unmarked circles should really be 
marked with a plain stroke or with a crossed stroke we 
cannot say whether it is true or false that some S's are 
not P, We cari tell, however, about the truth or falsity of 
A ; for if A were true and all S's were P, all the circles would 
have to be marked with a plain stroke, and that is not possi- 
ble so long as at least some of them are marked with a 
crossed stroke. Hence we can see from the symbols that 
represent the truth of O that A must be false. And so of 
the rest. 

So far no particular S has been definitely and individually 
designated. To indicate some particular individual or sub- 
group of individuals use, a small black dot or blacken the 
circle. All the remaining categorical propositions can then 
be symbolized. 

Singular A: Socrates is P ^ 

Singular E: Plato is not P ^ 

Exceptive A: All the S's but B are P (j)(|)<^or(:j)(j)0 
The first of these figures indicates ' All the S's but B are 
P (and B is not)', the second indicates ' All the S's but B 
are P (and it is not said whether B is P or not)'. 

Exceptive E : No S but BisP ^^^or^^^ 

Exclusive A: B is the only S which is P ^ ^ $ 

Exclusive E : B is the only S which is not P ^ $• c|) 

It is to be noticed that a person interpreting these diagrams 
could not distinguish between a proposition and its ' ob- 
verse' ; for example, between the affirmative proposition All 
S is P and the negative No S is non-P, or between the nega- 
tive No S is P and the affirmative All S is non-P. This is an 
advantage rather than a defect; indeed the whole value of the 
symbols rests upon such facts, for the difference between a 
proposition and its obverse expresses a difference of shading 
or accent in the thought, but not a difference in the objects 
thought about. The relations of the objects remain the 



120 THE OPPOSITION OF PROPOSITIONS. 

same whether they are told about in one way or in another, 
and the diagrams symbolize these relations as they are sup- 
posed to exist in the objects. They point to the reality with 
which thought is concerned and to which it must always 
conform whatever its shading, rather than to the particular 
shading which the thought may happen to take or the words 
in which it happens to be expressed, and they can be used 
to test the thought no matter what its shading or form of 
expression. 

The fact that these diagrams express no difference between 
a proposition and its obverse suggests the question that is 
sometimes discussed whether proposition A is not after all 
negative rather than affirmative. When we say that every 
nation prefers its own interests to the good of humanity 
(All S is P), do we have in mind all the nations that do this, 
or the fact that none can be found which does not ? Cer- 
tainly we cannot be sure that the statement is true until we 
find that there is no nation which does not (No S is non-Pj. 
Perhaps we can say that when proposition A expresses a 
hasty and unverified generalization it is affirmative, when it 
is derived deductively from general considerations it may 
also be affirmative, but when it is reached cautiously in the 
absence of general considerations it is usually negative. 
When we seek to verify a general statement, we do not count 
the cases in which it holds, but we look for exceptions."^ 

* This system of diagrams seems to me to indicate the opposition of 
propositions better than Euler's (explained elsewhere), partly because 
it provides a"<iiagram for every proposition, while his only provides for 
the first four, partly because the same diagram represents a proposition 
and its obverse, partly because the diagrams for all the propositions that 
express different facts are distinctly different, but mainly because it pre- 
serves the distinction between things and attributes, and represents the 
presence or absence of the latter in the former rather than the partial or 
complete inclusion or exclusion of one class by another. 



CHAPTER X. 
INFERENCE AND THE SO-CALLED LAWS OF THOUGHT. 

In previous chapters we have given examples of good and 
bad inference; we have said that all inference involves judg- 
ments about real or supposed objects of thought different 
from the judgments themselves; we have said that these 
judgments can be expressed in propositions, and in the 
chapter on the Opposition of Propositions we have had 
practical examples of the relation between the facts and the 
propositions about them. We must now inquire more fully 
what inference really is. In doing so we turn, though never 
altogether, from the question of words and their meanings^ 
and fix our attention more fully upon things and their 
relations. 

We infer when we suppose that because one state of affairs 

exists another exists also. The real or supposed facts that 

we reason from are called premises; those that , ^ 

^ Inference— 

we reason to, conclusions ; and we may say that what. 

the conclusion of any argument is true because the premises 
are true, or that the premises are true and therefore the 
conclusion is true. 

Clear as this matter seems it is not fully understood until 
we distinguish the relation of premise and conclusion from 
two other relations each of which may likewise be indicated 
by the words ' because ' and ' therefore ', namely, the rela- 
tion of cause and effect and that of motive and act. A 
man may say, for example, that he believes in Christianity 
because he was born and bred in a Christian community, or 

121 



122 INFERENCE AND THE LAWS OF THOUGHT. 

because he wants to go to heaven, or because the four 
gospels and the sacraments of the Church must have had 
some cause. The first ' because ' indicates a cause, the 
second a motive, the third a premise. The knowledge that 
such and such causes or motives exist may enable us to infer 
the existence of the corresponding effects or acts. If it is 
raining w^e know that people will put up their umbrellas. 
Similarly the knowledge that the effects or acts exist may 
enable us to infer the existence of the causes or motives. 
If people have up their umbrellas we know that it is raining. 
But with causes and motives as such, inference has no 
more to do than with any other relations. 

Inferences are usually divided into two classes: Deductive, 
or those in which conclusions follow so necessarily from 
their premises that their truth is as certain as that 
of the premises themselves; and Inductive, or 
those in which the conclusion follows from the premises with 
more or less probability, but by no means so inevitably — so 
that the premises might sometimes be true and yet the con- 
clusion be false. To illustrate the latter first : from the 
presence of dark clouds and a moist atmosphere we can infer 
that it will rain, but we cannot be certain of it. On the 
other hand, if we know that on cloudy days it always rains 
and that to-day it is cloudy, we can be quite certain that 
there has been or will be rain to-day. 

Deductive inference is the only kind that logicians dis- 
cussed for two thousand years. All that we shall have to 
say in the next seven chapters has direct reference to it. 
Induction will be discussed afterwards; something also will 
be said about the relation between the two kinds of infer- 
ence. In the meantime we need only say that there is not 
nearly so much difference between them as has often been 
supposed. 

Deduction, or the absolutely indisputable kind of infer- 
ence, does not depend, as most logicians have assumed, 
upon any special relation between our thoughts, but — like 



DEDUCTION. 123 

the other kind — it depends upon the nature and inner rela- 
tions of the objects thought about. It can be drawn only 
when the state of affairs asserted by the premise or premises 
could not possibly exist without the state of affairs asserted by 
the conclusion, or in other words, only when what is asserted 
by the premise or premises and what is asserted by the con- 
clusion are different aspects of some wider system in which 
the former could not exist without the latter. If the hne A 
cuts the line B we can infer with absolute certainty that the 
line B cuts the line A, because one cannot cut the other 
without making some such figure as this -[-? hi which the 
other also cuts the one. 

To take another example: If any one is told that three 
athletic teams, A, B, and C, each played three games with 
each of the others, that there were no drawn games, and that 
A won twice and twice only from B and twice and twice only 
from C, while B won only once from C, he has been told 
enough to enable him to construct a general scheme of 
things that includes also the number of games won by C and 
the relative standing of the teams : facts about which he was 
told nothing, and which even now some reader may not take 
the trouble to work out. That it can be worked out is not 
due primarily to any relation between the ideas merely as 
ideas of the person working it out ; but it is due to the fact 
which he knows, and which would exist whether he knew it 
or not, that when a contestant plays a game which is not 
drawn he must either win it or lose it, and if he does not 
win it his opponent does, and to the known relations of 
number. If the rules of the game made it possible for both 
sides to win or for both to lose, or if two from three left tw^o 
instead of one, the reasoning to be correct would have to 
take these facts into account and the conclusion would be 
different. 

A curved surface cannot be concave on one side without 
being convex on the other; and in general the nature of 
things is such that every variation in one aspect of a complex 



124 INFERENCE AND THE LAWS OF THOUGHT. 

state of affairs involves a corresponding variation in some 
other aspect. To infer we must know what some one aspect 
of the situation really is and the rule according to which it 
involves another aspect. Our knowledge of the first aspect 
is the premise of our reasoning, and from our knowledge of 
this aspect and of the rule we can reach the conclusion, or 
a knowledge of the other aspect. But if various aspects of 
a situation did not involve each other whether we reasoned 
about them or not, we should not be able to reason at all. 

It is thus not the business of logic — or of any part of it — 
as most writers have said that it is, to describe ' necessary 
forms or laws of thought' connecting one idea with another, 
but rather to direct attention to the most fundamental laws 
or relations of things which all reasoning takes for granted 
and which alone make it possible for any one state of affairs 
to involve any other. 

If this is a correct account of the nature of inference in 
general, the only way to test the validity of any specific case 
of inference is to ask : Is there any possible way in which the 
relations asserted in the premises could exist in the absence 
of those asserted in the conclusion .? Is it possible for one 
and the same object or general state of affairs to have the 
one set of relations without the other also ? If it is possible, 
then the denial of the conclusion may be consistent with the 
affirmation of the premises; if it is not possible, this denial 
is not consistent, and the QOYiQ\\x^\OYi follows. 

Logical Consistency is thus a matter of possibility and 
impossibility in the objects under discussion. This will 
become clearer as we proceed. 

Though the ultimate justification of every act of inference 

must be found in the nature of the things about which the 

inference is drawn, it would not be possible for 

* Laws of us to draw an inference unless we were able to 

^^^ * think of these things in some coherent and 
rational way. The fundamental elements involved in all 
such coherent and rational thinking are known as the ' Three 



THE THREE a.AWS OF THOUGHT'. 125 

Laws of Thought ' ; and we must now explain what these 
so-called laws of thought really mean. 

The first of these is called the Law of Identity; it is 
usually stated in some such form as this: * What is, is', 
* A is A ', ' Everything is what it is ' ; and this law with the 
two others are treated as axioms or first principles to which 
doubtful arguments should be referred, and by which alone 
they can always be tested. 

This first law of thought — the law of identity— does not 
mean that objects cannot change or cease to exist, that A 
cannot become B or be wiped out of existence altogether, 
that what is true at one moment is always true. It merely 
expresses the fact that we know what we are thinking about 
and w^hat w^e are thinking about it; that we can recognize 
an old object of thought as the same even when what we 
think about it is not the same, and that m a similar way we 
can recognize whether a new statement about it is or is not 
the same as an old one. We can consider an object or a 
situation in as many aspects as we please and still recognize 
that we are concerned with the same object or situation. 
A person can say, for example, that a certain house is red, 
that it is four stories high, that it is old, and that it was once 
inhabited by George Washington; and the speaker and his 
hearers can both recognize that he is talking about the same 
house all the time. But if he should add something about 
its pale-green color, its snowy peaks, its delicious flavor, its 
angry billows, its flushed and anxious countenance and its 
relation to the square root of the difference, we should then 
say that his mind was wandering, his thought was not con- 
secutive, his various ' its' did not refer to the same object. 
We, the hearers, could say that the objects referred to must 
all be different, but if the speaker's mind were really wander- 
ing, if he were utterly incapable of holding fast to an old 
object of thought and identifying it, he would not know 
that his various sentences referred to different objects, for 
without the power to identify an old object of thought he 



126 INFERENCE AND THE LAWS OF THOUGHT. 

would have no more idea of difference than of identity. To 
him no pronoun could have an antecedent and the words 
' same ' and ' different ' would be absolutely meaningless. 

This illustration has particular reference to the object 
thought about, but the power of remembering and recogniz- 
ing statements made about it is just as essential to sanity. 
The law of identity thus expresses the fact that thought 
points to objects and that we can know or recognize what 
objects we are thinking about and what we are thinking 
about them. 

The second ^ law of thought ' is called the Law of Contra- 
diction, and is expressed in such formulae as these : * Nothing 
can both be and not be', ^A is not not-A ', ^ xA cannot be both 
B and not-B '. While the law of identity rests upon our power 
of identifying an object of thought, the law of contradiction 
rests upon our power of distinguishing between an affirmation 
and a denial, between the meaning of 'is' and the meaning 
of ' is not ', of 'yes ' and of ' no '. The law, in its primary 
sense, at least, simply means, — what everybody knows, — 
that we cannot both affirm and deny the same thing about the 
same object. Understanding by S whatever can be named 
in the subject of a sentence, and by P whatever can be named 
in the predicate, the law means: If it is true that S is P, then 
it is false that S is not P and if it is true that S is no/ P, 
then it is false that S is P. The law as thus stated does not 
depend upon any particular knowledge about things ; it fol-. 
lows inevitably from the nature of thought. Why thought 
should take the form of a judgment, and why affirmative and 
negative judgments should exclude each other we do not 
know, but as soon as we know anything about ourselves we 
know that such is the case. 

There is a secondary meaning often attached to the law of 
contradiction, namely : that we must not ascribe incompat- 
ible qualities or relations to the same object. According to 
the primary sense of the law we contradict ourselves if we say 
that a certain thing is white and that it isn't white ; accord- 



TPIE THREE 'LAWS OF TI10U(.in '. 127 

ing to the secondary sense we contradict ourselves if we say 
it is white and that it is black. In the first case we had in 
mind the same quality — white, and the law said we could not 
both affirm and deny it ; in the second case we had in mind 
two different qualities, and the law said we could not affirm 
them both. In the first case the sense of contradiction is due 
to the fact that it is mentally impossible to affirm and to deny 
the same thing at the same time, just as it is physically im- 
possible to say yes and no at the same time, to nod the head 
and to shake it, to approach or draw a thing toward you and 
to recede or push it away ; in the second case it rests upon 
our knowledge that the same object cannot have two different 
colors at once. In the first case the contradiction rests upon 
the nature of a judgment and could be recognized by any one 
who could distinguish between the meanings of ^ is ' and 
Ms not', however limited his experience; in the second 
case it rests upon the nature of things as people gifted with 
sight believe them to be. 

If we did not believe in the existence of a world so con- 
stituted that the presence of any quality in a thing excludes 
certain other qualities, we should not recognize any con- 
tradiction in saying that a thing is both white and black, 
three feet long and one inch long, round and square, before 
and after. 

The qualities which do not, or cannot, exist together 
in the same thing happen to be those which appeal to 
the same sense, and which we are therefore able to com- 
pare together, and for which we usually have some general 
name, such as * color ' , ' size ' , ' shape ', ' time ' , ^ place ' . 
Incomparable qualities, such as red and square, may or may 
not coexist in the same object, and we have no difficulty 
in imagining any combination of them. Either because of 
the nature of our faculties or because of the limitations of 
our experience, we cannot imagine an object which has at 
the same time two different qualities of the same general kind. 

Because we cannot imagine a thing to have at once two 



128 INFERENCE AND THE LAWS OF THOUGHT. 

qualities of the same general kind, we assume that such quali- 
ties cannot really coexist, and when we assume this, it follows 
that to affirm one quality of an object is equivalent to deny- 
ing another, so that when any one says that a thing is large 
and small, white and black, we take it for granted he means 
that it is large and isn't large, that it is white and isn't white, 
and that he is therefore contradicting himself. Thus through 
the limitations of our imagination the law of contradiction, 
which in its primary sense is concerned only with the imposi- 
bility of both affirming and denying the same quaUties or re- 
lations, comes to take on a secondary meaning concerned 
with the inconsistency of affirming certain different qualities 
or relations.^ It is this secondary sense of the law that is 
expressed in the last two formulae I gave for its expression. 

The third general principle or law of thought is called the 
Law of Excluded Middle. The usual formula is ^ Everything 
must either be or not be ', ^ A must be either B or not B '. 
This law is the complement of the Law of Contradiction and 
means that every statement must be either true or false. If it 
is false that S is P, then it is true that S is not P, and if it is 
false that S is not P, then it is true that S is P. This law, 
like the law of contradiction in its primary and proper sense, 
is not derived from an examination of things, but follows in- 
evitably from the nature of thought in judging ; for not only 
do afftrmative and negative judgments necessarily exclude 
each other, as the law of contradiction says, but every pos- 
itive or active judgment must either affirm something or deny 
it ; there is no middle ground. 

Like the law of contradiction, the law of excluded middle 
has also acquired a secondary meaning, concerned not with the 
difference between affirmation and negation, but with the 
mutual implications of various qualities and relations in the 
objects judged about. 

* If we distinguish between the copula and the predicate we can say 
that in its primary sense the law is a mere matter of the copula; but in 
its secondary sense is made a matter of the predicate. 



THE THREE 'LAWS OF TlIOUCillT '. 129 

Experience teaches that every real thing, indeed every 
object of which it is possible to think at all, has qualities and 
relations of some kind. If it is not large it is small, if it is 
not here it is elsewhere ; or else it is a spirit or some other 
kind of immaterial object existing without space -relations, 
but not without the moral or other relations which that kind 
of immaterial objects possess. In general, if any object, S, 
has not a certain quality or relation, P, it must have some 
other quality or relation incompatible with P, and which we 
may therefore call not-P or non-P. To put it more briefly : 
If S isn't P it is non-P; every S must be either P or non-P ; 
and to say that S isn't P is equivalent to saying that it is 
non-P. 

This is the secondary sense of the law ; and it does not 
depend, like the primary, wholly upoii the mere nature of 
judgment, but partly also upon the fact that we have never 
found and cannot think of an object that does not possess 
some definite relation or other. 

But there is often still a third implication which the law 
seems to cover. 

From earliest childhood we find those about us dividing 
objects into various kinds, and in the course of experience we 
learn to take it for granted that however much they may 
differ from each other all objects of the same kind are deter- 
mined in the same respects ; have the same kind of qualities 
and relations. Every man has some moral standing. Hence 
if he is not good he must be bad. He has some color. 
Hence if he is not white he must be black, brown, yellow, 
or red. And so of size, weight, and all the other gener:il 
qualities which every man possesses. 

Now, as it happens, it is just as easy to find out that some 
object, say the soul or the square root of 33, has no color or 
weight or shape at all as to find out that it is not red or heavy 
or round, and in ninety-nine cases out of a hundred it is a 
great deal more serviceable to say so. Consequently when 
any one says that some object, X, is not red his hearer takes 



130 INFERENCE AND THE LAWS OF THOUGHT. 

it for granted that he is talking about an object that has some 
color or other, since otiierwise he would have said it was 
colorless.* And so of eveiy other quality and relation : we 
interpret the statement ^ S isn't P' to mean that S has some 
quality P' or P", which, though different from P, belongs 
to the same general class. 

The third matter which the law of excluded middle seems 
to cover is thus a rule for the interpretation of language. 
But such a rule is by no means infallible. It is quite possible 
to say that a triangle is not virtuous without the slightest 
intention of implying that it is vicious. 

Assuming the truth of the law in the secondary sense, and 
understanding that the phrase non-P is used to indicate some 

quality or relation incompatible with P, we can 
Obversion. ^ -^ ... ... . 

turn every aitirmative proposition into an equiva- 
lent negative, and vice versa : ' All S is P ' (A) into ' No 
S is non-P '(E); ' Some S isn't P ' (O) into ' Some S is 
non-P' (I); ^ All men are mortal' into ^ No men are im- 
mortal '; and vice versa. 

The manipulation of propositions in this way is called Ob- 
version or Immediate Inference by Priviiive Conception. It is 
less commonly known as Permutation or Infinitation. If we 
wish a formal definition we can say : 

To OBVERT a proposition is to deny or affirm the absence 
or presence of a relation whose presence or absence the orig- 
inal proposition affirmed or denied. 

* ' ' No one would be so foolish as to deny what no one could have the 
slightest temptation to affirm. If I say, then, that X is not Y, I imply 
that there are certain elements in X, by which, if they were taken alone, 
it might be confounded with Y. Of course the elements of resemblance 
may be comparatively few, but something in this case must have oc- 
curred to bring it into prominence." C C. Everett, " Fichte's Science 
of Knowledge ", p. 103. 



CHAPTER XI. 

IMMEDIATE INFERENCE, OR INFERENCE FROM A SINGLE 

PREMISE. 

When an inference is drawn from a single premise it is 
called immediate^ when from several premises taken together, 
mediate. The terms immediate and mediate as thus used 
have only a secondary reference to time. Their main 
object is to indicate the absence or presence of some inter- 
mediate process. Where an inference rests upon several 
premises and cannot be drawn from one of them alone, the 
intermediate process consists in constructing a notion of a 
total state of affairs according to specifications part of which 
are laid down by one premise and part by another. It is 
this total state of affairs in which alone both or all the pre- 
mises can be realized that implicates the conclusion. A 
state of affairs in which none or only a part of the premises 
were realized might implicate it, but we know that this other 
must. 

We are at present concerned with immediate inference, 
or the cases in which the state of affairs described by a single 
premise necessarily implicates that described in the con- 
clusion. 

The most interesting and important kind of immediate 

inference is called ^Conversion'. In discussing obversion 

we saw how it was possible to pass from one 

^ 11- Conversion. 

statement to another about the same object ; m 

conversion we feel warranted in passing from a statement 

131 



13^ IMMEDIATE INFERENCE. 

about one object or kind of object to a statement about an- 
other object or kind of object about which something has 
been impHed, though not directly said in the statement 
about the first object. If, for example, we should happen to 
know that some white things are square we should be able 
to infer that some square things are white. To be white and 
to be square are two very different matters ; but yet the 
world and our minds are so constituted that a statement 
about the one class of objects may serve as the basis for a 
statement about the other.* In like manner, if a person 
interested in the city of Cleveland should be told that it is 
183 miles west of Buffalo and he should afterwards have 
occasion to tell all that he knew about Buffalo, he would be 
able to say that it is 183 miles east of Cleveland. If he were 
interested in places 183 miles west of Buffalo he would be 
able to say that at least one of them was Cleveland. And if 
he were interested in the distance of 183 miles he could say 
that it is as far as from Buffalo to Cleveland. — The first 
statement was about Cleveland ; but the fact asserted was of 
such a nature that it could not be true unless the other state- 
ments, not about Cleveland but about Buffalo and places 183 
miles west of Buffalo and the distance of 183 miles, were 
also true. 

The doctrine of conversion found in most text-books on 
logic provides for only one of the three inferences which is 

here drawn, namely: a place 183 miles west of 
traditional Buffalo is Cleveland. The reason for this lies in 

the traditional way of dividing every proposition 
into subject, predicate, and copula, and of regarding the 
copula as a perfectly colorless sign of affirmative or negative 
predication. Every proposition was regarded as a kind of 

* The constitution of the world involved in this particular case is the 
fact that several attributes (<?.^. , whiteness and squareness) may be 
possessed with equal intimacy by the same object ; in the case about to be 
mentioned it is the fact that relations are reciprocal — facts of so familiar 

kind that we forget the debt our logic owes them. 



THE TRADITIONAL TREATMENT. 133 

equation of which the copula supplied only the idea of 
equality or non-equality. Our original proposition, divided 
in this way, would read 

Subject. Copula. Predicate. 

Cleveland is (a place) 183 miles west of Buffalo, 
and it would be regarded as meaning nothing more than that 
Cleveland was identical with a-place-183-miles-west-of-Euf- 
falo. Regarded in this way the proposition says nothing 
whatever about Buffalo or about 183 miles, but only about 
Cleveland and a place 183 miles west of Buffalo. These are 
the terms, and they cannot be broken up, consequently the 
only inference to be drawn, if inference it is, except by 
ob version or by way of opposition is found by reversing the 
equation, and saying a place 183 miles- west of Buffalo is 
Cleveland. 

According to the same way of regarding things the propo- 
sition * John is riding a horse ' can be converted into ^ a 
person riding a horse is John', but the traditional rules of 
logic make no provision for any inference about the hors' -'' 

* This limited view of the meaning of propositions can be easily ex- 
plained. In an age like that of Plato and Aristotle when scientific knowl- 
edge was thought to consist merely in description and classification, it was 
natural enough to overlook all the relations asserted in propositions except 
those of substance and attribute and individual identity, for the causal 
and other outer relations between things had no scientific significance 
except as indicating qualities o/t\\Q things, by which they could be iden- 
tified and classified. From this point of view the statement that John is rid- 
ing a horse is of value only as it tells one of John's accidents or occasional 
states by which he might perhaps be identified or distinguished from 
other people who never ride or at least did not ride at the time referred 
to. From the same point of view the converse statement that a horse is 
being ridden by John has scientific significance only as indicating that 
horses, or at least this particular horse, can be described as capable of 
being ridden or as having been ridden. This standpoint lent itself only, 
too easily to the purely mechanical and verbal treatment of propositions 
which is still common. Certainly with modern writers this purely verbal 
treatment of logical processes is only a pedagogic device. Yet it seems 
to me that it limits the usefulness of logic and that the subject is capable 
of being treated more directly. 



134 IMMEDIATE INFERENCE. 

If one were interested in describing John the facts would 
naturally be stated in one way; if he were interested in de- 
scribing the horse they would be stated in the other way. 
But the mode of statement was settled before the logical 
process began. It was with the description and classification 
of things, not with their outer relations, that logic was con- 
cerned. It therefore never occurred to the early logicians 
that it was a part of their business to show how the state or 
relations of one thing at any particular time involved corre- 
sponding conditions in something else. Except as they con- 
tained data for classification the mere spatial and temporal 
and causal relations of things had no logical import and 
were not worth analyzing. It was with descriptions of 
things, not with events, that the logical process began. 

Let us assume for a time, with the old logicians, that our 
only logical interest lies in the description and classification 
of things, and that every proposition with which logic deals 
must contain a subject, a predicate, and a copula whose sole 
function is to affirm or deny an equality or identity between 
the subject and predicate. If a proposition has not such a 
form it must be given one before it is dealt with logically, 
so that instead of saying ' John runs ', and ' Ducks like 
water ', we must say ' John is running ', or more properly 
' John is a creature who is running ', and * Ducks are 
creatures who like water '. 

The first thing to be noticed from this standpoint is that 
description merges insensibly into classification. When we 
say that ducks like water we undoubtedly describe one of 
their characteristics; but when we say that they are ' creatures 
who like water ' we may be regarded as classing them with 
other creatures who like it (if such exist) as distinguished 
from those who do not. Thus the many relations really 
expressed in propositions are reduced for logical purposes to 
one; when the traditional logician says that any object or 
class of objects, S, is P, all he means is that the object or 
class S is contained in the class P. 



THE TRADITIONAL TREATMENT. 135 

What does this statement about S enable us to say about 
the class P? — This is the question of conversion. '* A 
proposition is said to be converted when its terms are trans- 
posed, so that the subject becomes the predicate and the 
predicate the subject" (Fowler, p. 80). Converting the 
proposition ' S is P ' in this way we get ' P is S '. But how 
many of the P's are S ? From the fact that all ducks like 
water it does not necessarily follow that every creature that 
likes water is a duck. 

Sir, I admit your general rule,. 
That every poet is a fool ; 
But you yourself will serve to show it 
That every fool is not a poet. 

The mediaeval logician sought mechanical rules for 
manipulating words, and so he asked ' Is there any rule by 
which we can tell the quantity and quality of propositions 
that have been converted ? \ and he found two which could 
always be followed with safety: 

" I. The quality of the proposition (affirmative or nega- 
tive) must be preserved, and 

" 2. No term must be distributed in the Converse, unless 
it was distributed in the Convertend " (Jevons, p. '^z). 

The convertend means, of course, the proposition that is 
to be converted; and the converse that obtained by convert- 
ing it. A term is said to be distributed when used in such a 
way as to necessarily include all and not merely some of the 
members of the class it denotes. The subjects of the 
propositions A and E are thus said to be distributed; the 
subjects of I and O to be undistributed. But how about 
the predicates } 

When anybody who has not studied logic says that ducks 
like water, he uses the term ' ducks ' demonstratively, and 
he can tell fairly well whether he means to speak of all, or 
of only sovie or 7nost, of the creatures that the name denotes. 
The other two words in the sentence — ' like water ' — he uses 
descriptively to tell something about the ducks. If he is 



136 IMMEDIATE INFERENCE. 

now told that he was really talking not only about ducks 
but also about a class of -' creatures that like water ', and 
is asked whether he refers to all or only some of this class 
of creatures, he cannot help being puzzled, for the thought 
of such a class probably never entered his mind. That is 
the objection to what Sir William Hamilton and others have 
called the Quantification of the Predicate. But if he is com- 
pelled to answer, the only safe thing to say is that he means 
that ducks are at least some of the creatures that like water. 
Then his statement about the ducks will be true whether 
other things, such as gulls and frogs and fishes, happen to 
like water or not. To put the matter generally : Affirmative 
propositions, whether universal or particular, do not distribute 
their predicates. 

To convert an affirmative proposition we must therefore 
reverse the subject and predicate, retain the affirmative 
copula (rule i), and see that the subject is undistributed, 
i,e., that the proposition is particular (rule 2). In other 
words, the converse of A or I is always I. 

When a universal proposition is converted into a universal 
-* a particular into a particular it is said to be converted 
simply; but when a universal is converted into a particular 
it is said to be converted per accidens or by limitation. It 
will be noticed that when A is converted into I it cannot be 
converted back again into A, but only into I. From the 
fact that 'all Rhode Islanders are Americans', it follows 
that ' Some Americans are Rhode Islanders ' ; but all that 
can be inferred from the latter proposition is that ' Some 
Rhode Islanders are Americans '. 

In contrast with affirmatives, negative propositions always 
distribute their predicates. The statement that no cats like 
water means that cats and creatures that like water form two 
wholly distinct classes, and that no individual belongs to 
them both. We can therefore be as sure that no single 
creature that likes water is a cat as that no single cat is a 
creature that likes water. Thus the converse of E {e.g., No 



THE TRADITIONAL TREATMENT. I37 

cats like water) is always E (No creatures that like water are 
cats). 

The other negative proposition, O, is harder to deal with. 
*' In attempting to convert the proposition O we encounter 
a peculiar difficulty, because its subject is undistributed; 
and yet the subject should become by conversion the predi- 
cate of a negative proposition, which distributes its predi- 
cate'' (Jevons, p. S^). If certain boys, A, B, and C, do 
not like water we can be quite sure that no creature that likes 
water is one of these boys A, B, and C. Here it is easy 
enough to convert; but the statement that A, B, and C do 
not like water is equivalent to three singular propositions, 
not to a particular. If it had been forgotten who these boys 
were, one might still be sure that some boys do not like 
water (proposition O) ; but all that could be said on the 
strength of this about creatures that like water is that none 
of them are some boys or other. We could not say that 
none of them are boys. We might say, to be sure, that 
some of them are not boys, but this would be on the strength 
of what we know about cats and monkeys, not on the 
strength of the statement that some boys do not like watei. 
Since the statement that no P is some S or other convevs 
practically no information whatever about P, we must con- 
clude that /he proposition O ca7inot he converted: nothing 
definite can be said about either some or all of the objects 
denotable * by its predicate. 

Many logicians say in substance that though O cannot be 
converted in the usual way we can " apply a new process, 
which may be called conversion by negation, and which con- 
sists in first changing the convertend into an affirmative 
proposition, and then converting it simply '' (Jevons, p. '^2>), 
In this way ' Some boys do not like water ' becomes 
* Some boys dislike water', and converting this we get 

* I say denotable rather than denoted, because the predicate of a 
proposition is usually used to describe the things pointed out by the sub- 
ject, not to point out new ones. 



t^B IMMEDIATE INFERENCE. 

* Some creatures that dislike water are boys \ (Some S 
isn't P = Some S is non-P = Some non-P is S.) 

This so-called conversion by negation consists simply in 
converting the obverse; and it is a process which can be 
applied just as well to A and E (though not to I, whose 
obverse is O and inconvertible) as to O. 

The process of alternate obversion and conversion can 
be carried through various stages as follows; but it is valid 
only if the existence of all the objects named is presupposed: 

Proposition A. 

Beginning with Obversion. Beginning with Conversion. 

A. All S is P = A. All S is P r= 

E. No S is non-P ==: I. Some P is S = 

E. No non-P is S = O. Some P isn't non-S. 

A. All non-P is non-S = 
I. Some non-S is non-P — 

Some non-S isn't non-non-P, or 



' Some non-S isn't P. 

Proposition E. 
Beginning with Obversion. Beginning with Conversion. 

E. No S is P. E. No S is P = 

A. All S is non-P. E. No P is S = 

I. Some non-P is S. A. All P is non-S = 

O. Some non-P isn't non-S. I. Some non-S is P = 

O. Some non-S isn't non-P. 
Proposition I. 

Beginning with Obversion. Beginning with Conversion. 

I. Some S is P. I. Some S is P. 

O. Some S isn't non-P. I. Some P is S. 

O. Some P isn't non-S. 

Proposition O. 

Beginning with Obversion. Cannot be Converted. 

O. Some S isn't P = 

I. Some S is non-P = 

I. Some non-P is S = 
O. Some non-P isn't non-S. 



THE TRADITIONAL TREATMENT. 139 

Attention is directed to the fact that by this process of 
alternate conversion and obversion we are able on the 
strength of a given proposition to make assertions not only 
about objects to which the subject and predicate terms are 
applicable, but about objects — if we assume them to exist — 
to which one or both are wholly inapplicable [i.e., to 
non-A's and non-P's). We must, however, be very careful 
not to jump at conclusions of this sort. From the proposi- 
tion All S is P (All men are mortal) we can infer No non-P 
is S (No immortals are men), or All non-P is non-S (All 
immortals are non-human) ; but we cannot infer All non-S 
is non-P (All non-humans are immortals). 

The principal difficulty in conversion is due, as we have 
seen, to the fact that a descriptive predicate has to be turned 
into a demonstrative subject with the proper quantity. 
From this difficulty exclusive and exceptive propositions are 
free, since they always distribute their predicates. If Euro- 
peans alone are capable of self-government it must be that 
all races capable of self-government are Europeans. Indeed 
it is a rather curious fact that exclusive and exceptive 
propositions imply something about all the objects mentioned 
in the predicate and about all those not specially mentioned 
in the subject, but not necessarily about all those specially 
mentioned in the subject; so that the objects to which they 
seem to call special attention are those about which they say 
the least. From the supposed fact that Europeans alone are 
capable of self-government it follows, as we have seen, that 
all races capable of self-government are European; it also 
follows that no non-European races are capable of self- 
government; but it does not necessarily follow that all 
European races are capable of self-government. Because of 
this I am inclined to think that to transpose the subject and 
predicate of an exclusive or exceptive proposition is an 
analysis of meaning rather than a conversion. We cannot 
be sure that European races alone are capable of self-govern- 
ment unless we already know that all the races capable of 



I40 IMMEDIATE INFERENCE. 

self-government are European. The value of the exclusive 
form seems to lie in the contrast it brings out between the 
objects specially mentioned (to which the attribute in ques- 
tion at least may belong), and the rest of the class to which 
they belong — the kind of contrast which serves as the basis 
for all classification. 

The subject of conversion has been discussed so far from 

as mechanical a standpoint as possible. Fol- 
Tlie treat- , . , i j i • • i 

mentby lowmg the older logicians we have given rules 

for the manipulation of words which can be 

followed blindly. 

In the latter half of the eighteenth century Leonard Euler 
invented, or rather revived, a set of simple diagrams by which 
the relations between classes of objects could be so easily 
and so well symbolized that it was no -longer necessary to 
follow rules mechanically, or even to remember them at 
all. If the members of each class of objects are supposed 
to be enclosed in a circle, the visible relations of the circles 
can be relied upon to indicate the relations of the classes. 
When one class is included in (or is identical with) another 
(Proposition A), the circle S, supposed to enclose the mem- 
bers of the first, must be drawn inside of (or coincident with) 
the circle P, supposed to enclose the members of the 
second; when some members of the first class are also mem- 
bers of the second (Proposition I), at least a part of the circle 
S must lie inside of the circle P; when there are some mem- 
bers of the first class which are not members of the second 
(Proposition O), at least a part of the circle S must lie outside 
of the circle P; and when no member of the first class is a 
member of the second (Proposition E), all of the circle S 
must lie outside of the circle P. 

So far it has been the circle S w^e have discussed, as wholly 
or partly within or without the circle P. But we can neither 
draw nor conceive of figures so constructed that a circle S 
lies wholly or partly within another circle P without part of 
P's area lying within S. From * All S is P ' (Proposition A) 



THE TREATMENT BY DIAGRAMS. 



141 



or ' Some S is P ' (Proposition 1) wc can therefore infer 
* Some P is S ' (Proposition I). Similar grounds can be found 
in the space relations of the figures for the conversion of E 
(No S is P) into E (No P is S) ; while the figure only allows 
us to convert O (Some S isn't P) into the worthless Proposi- 
tion E, already referred to (No P is some S or other). 





Thus when we draw the diagrams we can convert without 
reference to the formal rules, merely by observing what the 
relations of the circles must be under the given conditions. 
This is a much more natural and rational process than to 
blindly follow mechanical rules. The only rule involved in 
the construction of diagrams in conversion or syllogism is 
this : Try to make them represent the premise or premises with- 
out at the same time representing any conclusion you have iji 
mind. If this cannot b,e done the conclusion follows. If 
it can be done it does not. 

Euler's diagrams have rendered great service to logic; but 
it must not be forgotten that in using them or any other 
diagrams constructed on the same principle we assume that 
spatial relations caft be relied upon to represent relations which 
are not spatial. Diagrams in logic are metaphors, and to 
reason in metaphors is usually extremely dangerous. Experi- 
ence happens to show that in the case of Euler's diagrams 
the metaphor is not misleading, but we must not forget on 
that account that it is usually better and safer when we can 
do so to reason about the relations of things themselves 
directly than through the mutual relations of their symbols. 



142 IMMEDIATE INFERENCE. 

The reason that Euler's diagrams seem to make logical rela- 
tions so clear is that they appeal directly to the senses, and 
that of all the relations perceived by sense those of space are 
the most constant, the most universal, and the most easily 
represented. Almost every conceivable relation thus comes 
to be symbolized in terms of space and seems to be better 
understood when it is expressed in spatial language. It is 
said that every preposition once expressed a spatial relation, 
and the same is true of very many words and phrases used 
with reference to the mental life {e.g., ' apprehend ', ' move- 
ment of thought ', ' idea m, or before the mind ', * convey an 
idea ', * express an emotion ', ' impression \ etc.). 

The great objection to Euler's diagrams is that, like the 
rules which they were intended to supplement, they apply 
only to relations of inclusion or exclusion between classes. 
Both are wholly inapplicable to either dynamic or non- 
dynamic relations between different individuals. Both, 
therefore, are of service within but a small portion of the 
whole sphere of thought. 

There is no reason why the term conversion should not 
be broadened so as to include the transposition of subject 
and predicate when the copula is understood to 
^eatment. express something other than mere identity or 
non-identity of things or classes. There are 
many propositions in which the subject and predicate name 
two different objects while the copula affirms or denies a 
dynamic or non-dynamic relation between them. The trans- 
position of the subject and predicate of such propositions 
might fairly be called conversion. The difficulty connected 
with the traditional conversion is to settle the distribution 
of the new subject; and it arises from the fact that a predi- 
cate used descriptively is turned into a subject used demon- 
stratively. With the kind of conversion jast mentioned there 
is no such difficulty, for in dynamic and non-dynamic 
propositions the predicate is already used demonstratively. 
Whatever mechanical difficulty presented itself would come 



A BROADER TREATMENT. 1 43 

from the copula. Sometimes it could remain unchanged 
and sometimes it would have to be altered so as to express 
a reversed relation. If John (subject) is-a-relative-of (copula) 
James (predicate), James is-a-relative-of John. Here the 
relation, so far at least as it is expressed, is the same for both 
parties and might be represented by an arrow pointed at both 
ends: John ^-> James; and the proposition can be converted 
by a mere transposition of subject and predicate. But if 
John is-the-father-of James we cannot infer that James 
is-the-father-of John. Here the relation expressed is different 
for the two parties and should be represented by an arrow 
pointing in one direction only: John -> James; and when we 
convert, the copula must be changed, so as to express the 
relation from the other side: James is-the-child-of John, 
James <^ John. 

When to reverse the relation expressed in the copula and 
when to leave it alone is a question that might be seriously 
considered if it were necessary or desirable to pay attention 
merely to our words and not to what they mean. But this 
is not necessary or desirable; and the question needs no 
serious consideration, for when we pay attention to the real 
object of discourse and understand the meaning of the words 
used there is no difficulty. 

Whether we use the term conversion in this broad sense 
or in a still broader sense to include statements about any 
objects on the strength of statements about other objects in 
which the first objects were mentioned, there is no general 
rule for conversion which can be followed blindly and no set 
of symbols which is always applicable. The only thing to 
do is to turn from mechanical rules and from symbols to 
the things themselves, find out exactly what relations are 
asserted of the object spoken about, and then ask ourselves 
whether there are not corresponding relations of other 
objects mentioned or implied without which the relations 
asserted could not possibly or conceivably exist. To do this 
we must imagine not only a single state of affairs in which 



144 IMMEDIATE INFERENCE. 

the asserted relations exist, but many; to find out whether 
there is not at least one (conceivable, or possible, or actual, 
as the case may be) in which the other relations that seem 
to be involved are not really involved. This is thinking, 
and no mechanical rules can save us the trouble. 



CHAPTER XII. 
MEDIATE INFERENCE AND SYLLOGISM. 

It has already been explained that mediate inference takes 
place when we recognize some new aspect of the total state 
of affairs in which alone all the relations asserted by two or 
more premises can exist together. To put the matter more 
concretely: Mediate inference takes place zvhen we conclude 
anything about the relations of tivo or more objects iu each other 
from the relations of each to some third object, the word 
* object ' being used in the broadest possible sense to include 
qualities and relations as well as things. From the fact that 
A is larger than B and that C is smaller than B we can con- 
clude that A is larger than C; and this is mediate inference. 

No inference can be drawn about the relations of two 
objects to each other, unless the object with Tini-taf 
which each of them is compared is in both cases of deduction. 
the same. From the fact that A is larger than B and that C 
is smaller than D, nothing can be inferred about the rela- 
tions of A and C. 

Moreover no inference can usually be drawn unless each 
of the two objects is compared with the third in the same 
respect; unless the relations discussed are homogeneous, or 
at least unless they belong to the same unitary system. 
From the fact that A is larger than B and that C is lighter 
than B, no inference can be drawn about the relations of A 
and C. Where Euclid says " Things which are equal to the 
same thing are equal to one another'', we must understand 

145 



146 MEDIATE INFERENCE AND SYLLOGISM. 

him to mean: *' Things which are equal to the same thing 
in any given respect are equal to each other in that respect '". 
A may be equal to C in physical strength, and B equal to C 
in intelligence without A and B being equal to each other 
in any respect whatever. In the same way the line AB may 
be equal in length and the line EF equal in color to the 
line GH, without their being equal to each other in either 
one or the other. 

While no inference is usually possible when the relations 
dealt with are heterogeneous, the inferences drawn when all 
the relations under discussion are homogeneous do not 
belong to formal logic. If A is B's landlord or creditor or 
agent, and B is C's, it is a lawyer's business, not that of the 
formal logician, to say whether A is in any sense C's landlord 
or creditor or agent ; if a substance D has a chemical affinity 
for E, and E for F, nobody but a chemist can tell whether 
D necessarily has or has not an affinity for F; if G is four 
times as large as H, and H is seven times as large as K, the 
relative sizes of G and K is a question of mathematics, and 
the traditional field of deduction is so limited that the formal 
logician as such is debarred from drawing a conclusion. 

In syllogism or the kind of mediate inference discussed in 
formal logic, two of the three relations usually involved in 
the premises and the conclusion are homogeneous, and the 
third is (or may reasonably be treated as) a relation of 
identity.* If we say * G is four times as large as H and H 

* I say ' two of the three relations usually involved ' because in a sorites 
there may be an indefinite number of premises. In this case the rela- 
tions stated in all the premises except the last must be relations of 
identity. 

The rule that two of the three relations must be homogeneous and the 
third a relation of identity does not exclude the case where all three are 
relations of identity, e.g., 'A is identical with R, and B is identical with 
C, therefore A is identical with C '. The most serious objection that I 
can think of to the rule as I have stated it seems to come from such cases 
as this: ' A is larger, taller, sweeter, heavier, better, prettier than B, B is 
larger, etc., than C^ therefore A is larger, etc., than C '. Ilere th? rela- 



LIMITATIONS OF DEDUCTION I47 

is seven times as large as K; therefore G is twenty-eight 
times as large as K \ the reasoning belongs to mathematics; 
but when we say ' G is four times as large as H, and H and 
K are one and the same thing; therefore G is four times as 
large as K ', the reasoning is syllogistic and belongs to deduc- 
tive logic. Similarly if we say * A is four miles due west of 
B and C is three miles due north of B, therefore A is five 
miles southwest of C ', the reasoning is geometrical; but if 
we say ' A is four miles due west of B, and C is three miles 
due north of B (i.e,, not at all west of B), therefore A and 
C are not the same ', the reasoning is syllogistic. Or to put 
it somewhat differently, if we say ' A is two miles w^est of B 
and three miles east of C, therefore B is five miles east of C ', 
the reasoning is geometrical or arithmetical and beyond the 
sphere of formal logic (not of course ' illogical '); but if we 
say ' A is two miles west of B and three miles east of C, 
therefore something two miles west of B is three miles east 
of C {i.e., one and the same thing is both two miles west of 
B and three miles east of C) \ the reasoning is syllogistic. 
In the examples of arithmetical and geometrical reasoning 
here given all the relations affirmed or denied were relations 
of size, number, or direction; but in the examples of syllo- 
gistic reasoning this was not the case. In the first of these 
three examples of syllogistic reasoning the second premise 

lions are all homogeneous and no one of them is a relation of identity ; 
and yet the conclusion seems to follow in each case from pure logic, and 
without reference to any special science. I suppose the answer to such 
an objection would be that before we speak of a thing as having more of 
a given quality than anything else we recognize that things can be ar- 
ranged in a series with reference to that quality, so that whatever goes 
beyond something else goes still more beyond the things which that some- 
thing else goes beyond. All that is implied by the use of the compara- 
tive — er or more — . So that when we say ' A is taller than B, and B is 
taller than C, therefore A is taller than C ', we might have said ' A is 
taller than B, and whatever B is taller than, C is a thing that B is taller 
than, therefore A is taller than C '. In the syllogism thus stated the 
second premise asserts a relation of identity and the rule holds good. 



t48 MEDIATE INFERENCE AND SYLLOGISM. 

affirmed a relation of identity and thus made the conclusion 
possible; in the second example the conclusion denied that 
two objects were identical, because they possessed incom- 
patible relations; in the third example the conclusion called 
attention to the fact that the objects described in the two 
premises were identical, so that the relations which they 
affirmed coexisted, or both belonged to the same object. 

The three examples of syllogistic reasoning which w^e have 
just given to illustrate the difference between such reasoning 
and that which is not syllogistic can also be used 
to illustrate the difference between three different 
kinds of syllogism, for there are certain respects in which 
they are quite different from each other. The examples 
were these : 

i) G is four times as large as H; 
H and K are one and the same; 
Therefore G is four times as large as K. 

2) A is four miles due west of B; 

C is three miles due north of B; 
Therefore A and C are not the same. 

3) A is two miles west of B; 

A is three miles east of C; 

Therefore something two miles west of B is also three 
miles east of C. 

In each of thesyllogisms there is a term (called the Middle 
Term) which occurs in each of the premises but not in the 
conclusion; but in the different syllogisms this middle term 
does not occur in the same place. In the first syllogism the 
middle term H is the predicate of the first premise and the 
subject of the second; in the second the middle term B is 
the predicate of both premises; and in the third the middle 
term A is subject of both. This difference of order is accom- 
panied by a corresponding difference of thought; and each 
one of the three syllogisms may be regarded as an example 



^FIGURES'. 149 

of one of the three ' Figures ' of the syllogism, which we are 
about to discuss. Most logicians say that there are four of 
these figures; but Aristotle gave only three, and as the fourth 
is easily derived from the others by a purely mechanical 
process, has no special function as distinguishea ^^rom the 
others, and is seldom or never. used in ordinary reasoning, it 
may easily be omitted. 



CHAPTER XIII. 
THE FIRST FIGURE OF THE SYLLOGISM. 

In the first figure the reasoning is of this sort. One 
premise, called the Major, asserts something about a certain 

object or certain objects; the other premise. 
General called the Minor, points out that one or more 

specified individuals are identical with some or 
all of these objects; and on the strength of this the Conclu- 
sion makes the statement contained in the major premise 
with direct reference to the individuals specified in the 
minor. Examples: 

None of the apostles were Gentiles; 
Peter was an apostle; 
. • . Peter was not a Gentile. 

Every one who has consumption has tubercular bacilli ; 
This patient has consumption; 
. • . This patient has tubercular bacilli. 

No Anglo-Saxon likes mob rule; 
Most Americans are Anglo-Saxons; 
. • . Most Americans do not like mob rule. 

Tt should be noticed that the major premise (which in 
each of these examples is written first) can affirm or deny 
any sort of relation whatever, while the minor always keeps 
saying: * This is he', 'This is one of them', 'These are 
some of them '. We may say if we like that in all typical 

150 



GENERAL FUNCTION. 151 

examples of the first figure the major gives a rule, and the 
minor points out that a certain case comes under it. 

In this figure the conclusion merely makes a specific or 
more specific application of what was said in the major 
premise to the objects specially mentioned in the minor. 
To do this, it substitutes the more specific term which occurs 
in the minor premise for the less specific term which occurred 
in the major; but in the conclusion the general sense of the 
major premise and its general arrangement of terms is pre- 
served. This is not true of any other figure. 

In the two other figures the distinction between major and 
minor premise is purely arbitrary, for both premises deal 
with the same kind of relations; the conclusion does not 
preserve the general sense of either; and one arrangement of 
terms in the conclusion is just as natural as the other. 

It should not be overlooked that when the major premise 
points out a relation of any sort between two objects or sets 
of objects the minor can specify any or all of the objects in 
question, and the specification is carried into the conclusion 
regardless of whether these objects were denoted by the sub- 
ject or by the predicate of the major. The following, for 
example, are perfectly valid syllogisms m the first figure: 

All Slavs hate all Semites; 

The Russians are Slavs and the Jews are Semites; 
. ' . The Russians hate the Jews. 

Oil and water will never mix; 
This is oil and that is water; 
. • . This and that will not mix. 

John is beating Thomas; 
Thomas is John's son; 
. • . John IS beating his son. 

John and Thomas are quarreling; 
Thomas is John's son; 
, • . John and his son are quarreling. 



152 THE FIRST FIGURE OF TME SYLLOGISM. 

If we use an arrow to indicate any dynamic or non-dynamic 
X'elation between two different objects and three horizontal 
lines to indicate identity and a bar across the symbol to 
indicate the absence of the relation, these four syllogisms 
would be represented in this way: 

Major: All Slavs -^ all Semites. 

Minors: Every Russian = a Slav. 

Every Jew = a Semite. 
Conclusion : . • . All Russians -> all Jews. 

Major: Oil < — > water. 

Minors: This = oil. 

That = water. 
Conclusion : This < — > that. 

Major: John -^ Thomas. 

Minor: Thomas = John's son. 

Conclusion : John -^ his son. 

Major: John < — > James. 

Minor: Thomas = John's son. 

Conclusion: John < — > his son.* 

Inference in the first figure amounts, as has been said, 
merely to this: Some or all of the individuals about which a 

statement has been made in the major premise 
Is there . ^ -r ^^ ■ \ - 

real are pomted out more specifically in the minor, 

inference? ^ , • i f • i 

and then m the conclusion the statement is 

made over again with specific reference to these individuals. 
The interesting question about it is whether in such a process 

* When we recognize that propositions expressing relations between 
different objects can be treated by the syllogism we must abandon, for 
such cases at least, the old rule that the major premise contains the 
predicate of the conclusion. In the third of these examples this rule 
would make what I have called the minor premise — Thomas is John's 
son — the major, though it is perfectly obvious that it is the other 
premise — ^John is beating Thomas — whose general sense is preserved in 
the conclusion. It is infinitely better to judge by the meaning than by 
the outward form. 



IS THERE REAE E\^FERENCE? i53 

there is any inference at all. Does not the conclusion merely 
repeat in other words a part of what has been already stated 
in the major premise ? And if so can this be called infer- 
ence ? Mill and others have maintained that it cannot. To 
get a fair view of the subject we must consider three slightly 
different sets of cases. Let us take an example of each. 

Peter, James, and John were all Jews; 
Peter is one of these; 
. • . Peter was a Jew. 

All of the apostles were Jews; 
Peter was an apostle; 
. • . Peter was a Jew. 

Whoever has consumption has tubercular bacilli; 
This patient has consumption; 
. • . This patient has tubercular bacilli. 

In the first of these examples no one would maintain that 
there is any inference. The conclusion merely repeats what 
has been said just as explicitly in the major premise. 

In the second example the case is somewhat different. 
No one who investigated the matter could be sure that all 
the apostles were Jews unless he were first sure about Peter 
and each of the others individually, but it w^ould be possible, 
nevertheless, to make a statement about all of the apostles 
without thinking about Peter and each of the others indi- 
vidually. If there is inference in this case it rests upon the 
curious fact that, by using such words as * all ' and ' every ', 
we can speak of each of a large number of individuals, 
though we do not, and cannot, have at once separate mental 
images of more than a very few of them. Such inference as 
there is consists in pointing out that the statement made 
applies to certain individuals that we may never have thought 
of when the statement was made — in realizing to some 
extent whom or what it was that was spoken about. If we 
adhere to our definition of inference as the recognition of a 
new relation of thmgs without which the relations asserted 



154 THE FIRST FIGURE OF THE SYLLOGISM. 

in the premises could not exist, this process is not inference, 
for the relation realized in the conclusion is not a new one; 
there is no new /^c/. But if we broaden our definition so as 
to include this realization of what has been said, though 
perhaps not realized, then of course there is inference; there 
is a new thought. Logicians who are mainly interested in 
their own mental processes are likely to admit this broader 
definition; those who are mainly interested in the relations 
of things are likely not to. 

In the third example the case is still different. When any 
one says that all of the apostles were Jews he means to 
include each member of a certain definite number of indi- 
viduals determined beforehand. He speaks demonstratively 
of certain individuals as such. The only question is whether 
or not he realizes as he should the identity of all the indi- 
viduals that he speaks about. But when any one says that 
whoever has consumption is suffering from the presence of 
tubercular bacilli, he is not pointing to certain definite indi- 
viduals determined beforehand. Rather he is speaking 
descriptively of any individual who happens to have con- 
sumption, no matter who he may be or how many there may 
be of them. To know that whoever has consumption has 
tubercular bacilli, one does not have to know first about 
each individual patient as such; he needs only to know that 
these bacilli are the sole cause of the disease. When, there- 
fore, he puts the two premises together and concludes that 
some particular patient has tubercular bacilli he has gained 
some knowledge that could not possibly have been derived 
from a mere analysis of the major premise. He has reached 
a new aspect of things — found a relation not previously 
mentioned — and has undoubtedly made an inference. 

Looking back at the three kinds of cases, we can see that 
in the first, where objects are individually specified in the 
major premise, the minor is superfluous, and in the conclu- 
sion there is no real inference. In the second, where a 
certain definite number of objects are mentioned in general 



PRINCIPLE AND CAUTIONS, 155 

terms in the major, the minor would be superfluous if we 
realized all that is said, and such inference as there is con- 
sists in realizing what is said. In the third, where the major 
expresses a general law applicable to every individual of a 
certain kind, the minor is not superfluous, and in the con- 
clusion there is real inference. 

From all that has been said it is evident that the principle 
upon which we reason in the first figure is as follows: W/ia/ 

IS true of an object specified in one way is true of 

r . r -, ' 7 Tr "' Principle 

the same object specified in any ottier way. It we and 

■^ , • , , • • cautions. 

omit the case in which the major premise is a 

singular proposition, the principle amounts to this: What is 
stated in a universal proposition is stated of every' object to which 
the subject term is applicable; or, less technically, What is said 
to be true of every member of a group (or of every object which 
possesses a given relation) is said about each 07te of them, 
eve?i though each is not separately thought of when the statement 
is made. 

So much for the principle. In applying it we must 
observe certain cautions. In the first place, if the major 
premise speaks only of certain unspecified members of a group 
— i.e., if the major is particular — we cannot be sure that any 
of the objects named in the minor, though members of the 
group, are objects spoken of in the major; and consequently 
no conclusion can be drawn. 

It IS true that some animals are fierce, and it is also true 
that all mice are animals; but it is not true that mice are 
fierce. If such a conclusion did happen to be true in any 
one case, that would not make it follow from the premises; 
for a conclusion does notfolloiv unless we can be absolutely 
certain that whenever premises of that kiiid 's.i^ true that kind 
of conclusion must be true also. 

If we use a number of small circles to represent animals 
of various kinds, and let a plain stroke drawn through a 
circle, (j) , indicate that the animal is fierce, and a stroke with 
a bar across it, ^ , indicate that it is not fierce, the major 



TS6 THE FIRST FIGURE OF TH^: SYLLOGISM. 

premise gives this picture: o (j) o ([) ([) o Some are said to 
be fierce, and of some nothing is said; so some of the circles 
are marked with a plain stroke and some are left unmarked. 

If now we indicate mice by thickened dots, we must put 
all the dots within the circles to indicate what is stated in 
the minor premise, that each mouse is identical with some 
animal ; but as there may be animals which are not mice, we 
must leave some circles without dots, thus; 0000 If 
it afterwards turns out that every animal is a mouse, we can 
fill in the remaining circles. 

Now if we indicate in a single set of figures everything 
which has been asserted and remember this rule: Do 7iot put 
more marks than you have to in any one circle, we get such a 
diagram as the following: o (|) c|) o 

Here dots and plain strokes do not coincide, but there is 
nothing in the diagram to indicate that they cannot. That 
wQuld be indicated by drawmg a crossed stroke (meaning 
not-fierce) through every dot, thus: o ([) cj) (^ (^ o The 
figure as it stands merely means that there is no evidence 
to show that any dot (mouse) must possess a plain stroke 
(fierceness). Whenever the major premise is particular it is 
possible to construct such a diagram. 

If in the example given the major premise had been uni- 
versal, every circle would have been marked, so that it would 
have been impossible to avoid putting the dots where they 
would also be marked; and so the diagrams would have in- 
dicated the conclusion that all mice are fierce : (^ ^ (|) (1) 

If the major premise is not particular, but the minor is, 
that is, if the minor says that some members of a second 
group belong to the group spoken of in the major but does 
not say which members of the second group these are,, then 
we can conclude that what was said in the major premise 
was said of some members of the group named in the minor, 
but we cannot possibly say which members they are. The 
objects cannot be designated any more definitely in the con- 
clusion than they were designated in the premise. If all 



PRINCIPLE AND CAUTIONS. '^ 157 

young animals like play and some mice are young animals, 
we can conclude that some mice like play, (j) (j) (i) • , but we 
cannot conclude that all mice like play or that any particular 
mouse likes it. In other words, if the minor premise is 
particular, the conclusion must be particular also. If we 
have no definite information to begin with, syllogistic manip- 
ulation will not supply it. 

Putting together what has been said about the two 
premises, our first caution is this: In the first figure if the 
major premise is particular, no conclusion can be drawn; if 
the minor is particular, the conclusion must be particular. 
This caution can be stated less mechanically and without 
regard to figure or distinction of premises as follows: 

i) A relation can belong to so7ne inembers of a group without 
belonging to all the members, to any given member^ or to any one 
of a given group of members. 

The phrase ' to all the members ' is really superfluous ; for 
no relation could belong to each member without belonging 
to a given member. What is true of all mice must be true 
of this mouse. The last words of the caution — '^or to any 
one of a given group of members " — are necessary in order to 
exclude a particular conclusion as well as a singular or uni- 
versal when the major premise is particular. 

The principle on which we reason in the first figure is 
quite as applicable when the major premise is negative as 
when it is affirmative. The proposition ' No men are per- 
fect ' states something about every man, not about no man. 
It means that every man is without perfection, and if we 
know Socrates to be a man, it is applicable to Socrates. 
If we represent the proposition by a diagram, we may cross 
our strokes to indicate that the objects represented have not 
the quality in question; but the strokes must be drawn 
through every circle, to indicate that every man is described, 
(^ ^ ^ , and the circle that stands for Socrates must be 
marked with the rest. 

But when the viinor premise in the first figure is 7iegative it 



153 THE FIRST FIGURE OF THE SYLLOGISM. 

does not come under the principle, and 7io conclusion can be 
drawn. If we know that all the apostles were Jews, it will 
not tell us anything about Job's race to say that he was not 
an apostle. The function of a minor premise in this figure 
is to point out particularly some of the things spoken about 
in the major, and if an object is not one of those spoken 
about in the major, then nothing has been said about it one 
way or the other. 

Clear as this is, there is a strong tendency in such cases 
to draw a negative conclusion, e.g., The apostles were Jews; 
Job was not an apostle; therefore Job was not a Jew. 
The caution against yielding to this tendency might run as 
follows: 

2) To say that something is t7'ue of cei'tain objects does not 
imply that it is false of others. 

The same tendency to draw negative conclusions where 
no conclusion at all should be drawn is found — though it is 
not so strong — where the minor premise is particular. If 
we are told that no men are perfect and that some rational 
beings are men, we have a right to conclude that some 
rational beings — namely, those that are men — are not perfect ; 
but we have no right to conclude that some rational beings 
— namely, those that are not men — are perfect. To do so 
is to ignore the caution just given. It also involves the 
other blunder of interpreting ' some are ' to mean ' some 
are and some are not \ The statement that some rational 
beings are men gives us no valid reason for believing that 
they are not all men. Both blunders are covered by the 
caution.* 

Here is a set of diagrams for the benefit of any one who 
may wish to compare them with his own. If we wish to 
include negative minors, we may draw a short stroke through 
one side of the circles to indicate something outside of the 

* The first caution covers fallacies of illicit ??mior and undistributed 
middle as they occur in the first figure ; the second caution covers 
fallacies of illicit major in the same figure. 



PRINCIPLE AND CAUTIONS. 



159 



group that the circles stand for, or something that does not 
have their qualities.* 

Major A and minor A 





E 






I 













A 






E 






I 













A 






E 





A 


^ ^ ^ 


Conclusion A 


A 


•I ^ (J) 


t ( 


E 


A 


(j) (}) 


" r 


ion( 


A 


^^00 


< < 


( ( 


I 


(]) (j) 4) • 


(< 


I 


I 


i i ^ • 


i i 





I 


4) . 


" I 


ion 


I 


^ • 


< (. 


< ( 


E 


(]) (j) . . 


«< 


< < 


E 


^ ^ • . 


, << 


< ( 


et cetera. 







* If we wished to distinguish in our diagrams between syllogisms in 
which the major premise describes objects as they are in themselves and 
those in which it tells of some causal or other relation between objects, 
we could indicate the latter in some such way as the following, using 
the arrow to indicate the relation : 



Every Slav hates every Semite O \ '^^-^ 



O 



O 
Every Russian is a Slav © V 

O ) 

(O 
Every Jew is a Semite -< O 

O 



O ) ( O 



Therefore every Russian hates every Jew, ^ 'b-^ -< O 

O ) ( O 

That is to say. The Slavs, including all the Russians, hate the Semites, 
including all the Jews. 

Every Slav hates every Semite, and some Russians are Slavs and 

o) (o 

some Jews are Semites © V )^^ < Q 

O 



In the text I have treated universal propositions as though they were 
nothing more nor less than statements about every member of a certain 



i6o THE FIRST FIGURE OF THE SYLLOGISM. 

group of objects, and have omitted any reference to the causal relation 
which they so often imply. (See above, p. 109.) 

The principle and cautions can be easily restated so as to take account 
of this causal relation, as follows : 

Any object or relation (S) which possesses or involves a given rela- 
tion (M) possesses or involves every other relation (P) which that rela- 
tion (M) involves, provided that M really (?.<f., necessarily or always) 
involves it. 

The fact that an object or relation (S) does not possess or involve a 
relation (M) which involves another relation (P) is no evidence that the 
object or relation (S) does not possess or involve this other relation (P;. 

The first paragraph covers the rule and the more important part of 
the first caution ; the second covers the second caution. To cover the 
rest of the first caution we must add that a statement about some un- 
designated member or members of a group of objects (S) will not enable 
us to say anything about any particular one of them. 

Here is an example of the sort of causal connections I speak of : 

Going to war involves danger for the soldier. 

Danger for the soldier involves distress for his family. 

. •. Going to war involves distress for the soldier's family. 

Each of the diagrams in the text is intended to represent at least one 
sample of every object mentioned in either premise, and to preserve 
the distinction between those that are described in a given respect and 
those that are not. I have tried to make the illustrations as concrete as 
possible by using closed figures — circles or dots- — to represent things, 
and lines drawn through them to indicate attributes. When the sense 
is once understood these circles are not so good as a matter of practical 
convenience as simple letters written one after the other with the under- 
standing that the first letter stands for a thing and those that come after 
it for attributes. AB would thus mean that all A's have the attribute 
B {i.e., are B's). A, AB would mean that some A's have the attribute 
B. A, ABC, BC, would mean that some A's are B and all B's are C, 
and that therefore some A's are C. When these letters are used, a 
stroke over a letter indicates the absence of the attribute in question. 
ABC, BC means that all A's are non-B, and all non-B's are C, and 
therefore all A's are C. 

When we use these letters it is easy to get from pictorial representa- 
tions to algebraic. A = AB means that every A has the attribute B, i.e., 
that every A is also B. 

The pictorial representations most used are Euler's. These do not 
attempt to represent individual objects or to preserve the distinction 
between things and attributes ; but deal with the mutual relations of 
classes, As the diagrams are drawn on precisely the same principle 



PRINCU^LE AND CAUTIONS. 



i6i 



for all the figures (including the fourth) there is no denying their con- 
venience for any one who has to work out a set of problems. Mere are 
some of the diagrams for the first figure. 



Major A 
Minor A 
Conclusion A 




Major E 
Minor A 
Conclusion E 




Major A 
Minor I 
Conclusion I 




Major E 
Minor I 
Conclusion O 




Major A 


/ ^ 


^^^ 


\ Major I 




Minor E 


;A?; 


Lv 


/ Minor A 


/-' 


Conclusion — 


V'- -, 


V / 


Conclusion — 


(<K 




(a?^ 


-<< 




'\f 




""— '' 


(A?) 




\ 




The dotted lines are used to indicate doubt as to where the circle or 
the part of the circle in question should fall. 



CHAPTER XIV. 
THE SECOND FIGURE OF THE SYELOGISM. 

In this figure each premise describes an object or set of 

objects, and from the nature of the two descrip- 
Function , . . ^,^ i ■, , 

and gfeneral tions the conclusion tells whether or not the 

objects are identical with each other. 

The man that came to my house was tall and thin; 
The man that went to your house was short and fat 
(i.e., not tall and thin) ; 
. • . The man that came to my house is not the man that 
went to your house. 

Crows do not sing; 
This bird sings; 
. • . This bird is not a crow. 

Whales suckle their young; 
Fishes do not: 
. • . Whales are not fishes. 

The second and third of these examples differ from the 
first in this respect: In the first, two given objects are com- 
pared, and we conclude that they are not identical ; in the 
second a given object is compared with a class of objects, 
and we conclude that it does not belong to the class — that 
it is not the kind of thing to which the class-name applies; 
in the third two classes of objects are compared. In the 
first case we are concerned with identification in the nar- 
rowest sense of the term; in the others with classification. 
In the general description of the figure I have mentioned 
only the identification because it is the more fundamental 

162 



FUNCTION AND GENERAL CAUTIONS. 163 

and the classification really depends upon it. If we could 
not distinguish between individual objects, we could not 
distinguish between classes. To say that whales are not 
fishes is to say that there is not any whale which is identical 
with any fish. To classify is thus merely to distinguish 
between individuals in groups, and the principles by which 
we distinguish classes are nothing more than those by which 
we distinguish individuals. 

In this figure, therefore, both premises are concerned with 
descriptive relations, and the conclusion with a relation of 
identity. * 

The next thing to be noticed about the figure is that the 
two premises must describe their objects in the same respect. 
If I describe the man I saw as tall, and you describe the one 
you saw as agreeable, the descriptions indicate absolutely 
nothing about the identity of the men. 

But even when both premises describe their objects in the 
same respect a conclusion is not always possible. If each 
of two persons had met a tall man named Smith, they would 
not necessarily have met the same man. Two Dromios or 
two atoms of hydrogen might have innumerable points of 

* For the purposes of this figure propositions which in themselves are 
not strictly descriptive are treated as such. When we conclude, for 
example, that Newhaven and New Haven are different cities because 
one is on the road from Paris to London, and the other on the road from 
New York to Boston, the geographical or spatial relations of each of 
them to the adjacent cities are practically regarded as a part of the 
city itself. The distance between Newhaven and London or Paris is 
a spatial relation and belongs as much to London or Paris as to 
Newhaven. But when it serves to distinguish Newhaven from New 
Haven it is treated as though it belonged, like its size or its history, 
to Newhaven itself. For this reason we make the word Newhiaven 
the subject of the sentence in which the facts are expressed. We do 
not say " London is a usual terminus for persons traveling from Paris 
and Newhaven", or ''A good way to reach London from Paris is 
through Newhaven ", or " London is so far from Newhaven and so much 
farther from Paris byway of Newhaven". What the syllogism in- 
volves is not the distance of London or Paris as such, but all of them in 
so far as they characterize Newhaven. 



1 64 THE SECOND FIGURE OF THE SYLLOGISM. 

resemblance and yet be two. As the points of resemblance 
between two complex things increase, the probability that 
the things are really identical also increases: but no amount 
of resemblance can supply theoretically absolute proof of 
such identity. The prisoner in the dock might bear every 
resemblance to the man who was seen reeling on the street 
the night before and yet possibly, though not probably, be 
a different man. We could be absolutely certain of their 
identity only if the reeling man had been arrested at the time 
and never lost sight of for a moment until he was placed in 
the dock. 

The fact is that the identity of two things involves a great 
deal more than mere resemblance, no matter how complete 
the resemblance may be. Consequently, though we can 
often prove that things are not identical from the fact that 
they are dissimilar, we can never prove that they are identical 
from the fact 'that they are similar. If men are mortal and 
angels are not mortal, it follows that men are not angels; 
but if men are mortal and horses are mortal, it does not 
follow that men are horses. In this figure negative conclu- 
sions alone are valid. 

There is no logical blunder more frequent than to conclude 
that because things are alike they are necessarily the same. 
Flour is white, says the child; what I see all over the ground 
is white; therefore what I see all over the ground is flour. 

Good dollars are silvery-looking discs bearing a certain 

stamp ; 
This is a silvery-looking disc bearing that stamp; 
. • . This is a good dollar. 

Benevolent people smile affably; 
This man smiles affably; 
. • . This man is benevolent. 

AllPisM; 
All Sis M; 

.-.All Sis P. 



FUNCTION ANO GENERAl. CAUTIONS. 165 

But what the child sees on tlie ground is snow, not flour, 
and sometimes our silver disc is counterfeit, and the smiling 
stranger a brute. S is not always P. 

The logical trouble comes when we mistake probabilities 
for certainties. In practical life it is usually better to take 
an occasional counterfeit coin than to msist upon testmg 
them all, better to be deceived m a character occasionally 
than to refuse all intercourse with one's fellows until they 
prove their right to be trusted, better to bow to a stranger 
than to cut a friend. But a good rule of conduct when we 
must act in a hurry is not necessarily a good rule of conduct 
or thought when we have time to-be careful. The bank 
teller must be on the watch for counterfeit money, the em- 
ployer of a confidential clerk must look behind his face, 
and the sheriff should be sure of his man. In the same 
way, as students of deductive logic we must reject all con- 
clusions that do not follow with absolute necessity from the 
premises.* 

* The significance of this fallacious reasoning A A A in the second 
figure may become clearer if we show its relations to the first figure. 
• In the second figure we say 

All Y is Z 
All X is Z 
. •. All X is Y 
Now if we could convert the first premise simply, i.e.^ without alter- 
ing the quantity, we should get a perfectly valid syllogism in the first 
figure : 

All Z is Y ^ ^ ^ 
All X is Z 
.-. All X is Y 
But we cannot convert the premise simply. All we can say is that some 
Z is Y, and from this major premise no conclusion can be drawn. 
([) O 

If we happened to know not only that some Z is Y, but that most Z is 
Y, we might conclude that X is probably Y. 

Most silvery looking discs bearing a certain stamp are good dollars. 

This is a silvery looking disc bearing that stamp. 

.'. This \^ probably a good dollar. 

Even as a rule for hurried action it is not wise to draw affirmative 



1 66 THE SECOND FIGURE OF THE SYLLOGISM. 

We have seen that in this figure no affirmative conclusion 
can be drawn — similar things are not necessarily identical. 
But how about the negative conclusion ? Can we say with 
any more certainty that dissimilar things are not identical ? 
Is not the tadpole of last summer identical with this 
summer's frog, the bright-winged bird of the spring with the 
sober-looking one of the summer, the grub of one month 
with the butterfly of the next, Saul the persecutor with Paul 
the apostle ? On the other hand, no one can suppose that 
the tadpole is identical with the later bird, or the grub with 
Paul, or even that a tadpole seen this morning is identical 
with a perfect frog seen this noon. The fact is that objects 
can be distinguished from each other by their qualities or 
relations only when these are different at one and the same 
instant; so that if the objects are not observed simultaneously 
we cannot distinguish them by their qualities or relations 
unless we believe these latter to be so permanent that they 
cannot be wholly changed in the time which has elapsed 
between the two observations. What qualities or relations 
are relatively permanent and what are not we can learn only 
through experience, without a constant appeal to which 
logic is perfectly helpless.* 

To sum up, the Principle on which we reason in the 
second figure is that Dissimilar objects are not identical; and 
these are the Cautions: 

3) Similarity does not prove identity. ^ 

4) Dissimilarity does not prove non-identity if the object might 
have changed, 

conclusions in the second figure unless we have reason to believe that 
the converse of the major premise is usually true. In other words, the 
only possible justification for such reasoning in the second figure is found 
in the fact that it sometimes represents a fairly good induction in the 
first figure. 

^ Of course it is only things that change and still retain their identity. 
Blue is not like yellow now, and never will be. 

•j- This caution covers the fallacy of undistributed middle as it occurs 
in the second figure. 



QUANTITY IN THE SECOND FIGURE. 167 

5) Different descriptions do not i?nply dissimilarity unless the 
relations described are incompatible. 

So far our examples have all dealt with universal or singu- 
lar propositions, and no difficulties have arisen 
from questions of quantity. It is clear that from Pjf the^^"^ 
universal or singular premises a universal or |^^°^^ 
singular conclusion can be drawn; but can we 
draw any conclusion at all from particular premises ? 

First, when both premises are particular. If some mem- 
bers of Congress have blue eyes and some lovers of literature 
have brown eyes, i.e,^ have not blue eyes, what inference 
can be drawn ? It is clear enough that certain members of 
Congress, namely, those with blue eyes, are not identical with 
certain lovers of literature, namely, those with brown eyes. 
Using the sign = to indicate identity and ^ to indicate non- 
identity, we can make such a diagram as this: 

Congressmen. Lovers of Literature. 

O O 

o o 

meaning that no one of the described congressmen is iden- 
tical with any one of the described lovers of literature. But 
for all we know, each one of the described congressmen may 
be identical with one of the undescribed lovers of literature, 
and vice versa, e.g., the first in one column with the third in 
the other, and so on. It might be that every congressman 
was a lover of literature and every lover of literature a con- 
gressman, in spite of the fact that a blue-eyed congressman 
is not a brown-eyed lover of literature. 

To put the matter somewhat differently. From the fact 
that certain S's are not identical w^ith certain P's, it bv no 
means follows that certain S's are not P's at all. Suppose 
every S to be a P as indicated below: 

S's. P's. 



^ 


— 


^ 


^ 


ZZ" 








^ 






1 68 THE SECOND FIGURE OF THE SYLLOGISM. 

The first S is identical with the first P, but for that very 
reason it cannot possibly be identical with the second or the 
third. If there are in all one hundred different S's and one 
hundred different P's, and if each of the S's is identical with 
one of the P's, then there are ninety-nine different P's with 
which that particular S is not identical. Jones the congress- 
man is identical with Jones the literary man, but not with 
Smith or Brown. 

As long as there are two or more S's it must necessarily 
be true that certain S's and certain P's are not identical, and 
it does not make any difference whether every S is a P, or 
no S is a P, or some S's are P and some are not. Hence the 
inference we seem to dsd.^ from two particular premises in the 
second figure — that certain S's are not identical with certain 
P's — does not follow from these premises any more than from 
any others in which several S's are mentioned. It is equiva- 
lent to the mere truism that no one S can be identical with 
more than one P. It is something we might have known 
long before we knew anything about the special facts stated 
in the premises. It is practically no inference whatever from 
these premises and we may as well say that from such 
premises no inference can he drawn. 

When one premise is particular and the other singular the 
case is much the same. If we have been told that some of 
the masqueraders at a ball were tall and if we know that 
John is short, we can be sure that John was not one of these 
tall masqueraders. We can say if we like that there were 
certain persons there with whom John was not identical ; but 
we know that already if we happen to know that there were 
more persons than one present. It doesn't depend at all 
upon the question of height. This inference is thus worth- 
less; and no other can be drawn. 

When one premise is universal the case is different. If 
everybody at the ball was tall and John is short, we know 



* ^ 



\ 



QUANTITY IN THE SECOND FIGURE. 



169 



that he is not identical with any one of them, i.e., he was 
not there. Similarly if we had been told that every one at 
the ball was tall and that there are some members of the 
club who are not tall, we could be sure that there are some 
members of the club who are not to be identified with any 
one who was at the ball, i.e., some members of the club 
were not at the ball. 

Club - S. At the ball - P. 






On the other hand we could not be sure that some of those 
at the ball were not members of the club. If some S's are 
M and no P's are M, or if some S\s are not M and all P's 
are M, it follows that some S's are not P's; but it does not 
follow that some P's are not S's, for it may be that each 
of the P's is identical with one of the undescribed S's, The 
S's. P's. S's. P's. 

^ \ f ^ \ [^ 

^\ ^ \^ [ ^ J * 

o 1 ^ O I (j) 

o I ^ O I ([) 

reasoning is valid only if you arrange your conclusion so as 
to have for its predicate the term which occurred in the 
universal premise. In the technical language of the syllo- 
gism : The major premise {i.e,, the one containing the predi- 
cate of the conclusion) must he universal. The difference 
between concluding that some S's are not P's and that some 
P's are not S's may become clearer if we remember that 
Proposition O cannot be converted. 

When both premises are universal it is clear enough that 
a universal conclusion can be drawn; and of course it makes 
S's. P's. S's. P's. 



170 THE SECOND FIGURE OF THE SYLLOGISM. 

no difference which of the premises is affirmative or negative, 
so long as the quality of the two is different. 

Putting all this together we can add another Caution: 

6) We cannot say that any S's are not P's unless each of the 
S's in question is different from every P,^ To put it some- 
what differently, Evidence siijficient to prove that some S's are 
not P's may not be sufficient to prove that some P's are not S's^ 
and vice versa. 

The general principle of the figure and the caution respect- 
ing quantity are worked out together in the following formula 
which a student may use if he likes instead of the separate 
statements : 

If all the members of one group differ in a given respect from 
all the members of another^ then no member of either group is a 
member of the other. If some members of one group differ from 
all the members of another^ then there are some members of the 
first group vohich are not members of the second; but it does not 
follow that there are members of the second which are not mem- 
bers of the first. The mere fact that some ?nembers of one 
group differ from some members of another proves that those 
particular individuals are not identical, but it does not prove that 
any member of either group is not also a member of the other. 

* This caution covers the fallacy of illicit major in the second figure. 
Illicit ininor is covered in the second figure as in the first by the first 
caution. 



CHAPTER XV. 
THE THIRD FIGURE OF THE SYLLOGISM. 

In this figure one premise asserts that a certain object pos- 
sesses (or does not possess) a given relation, and the other 

premise asserts that this same object possesses (or 
, XT.,. 1 Purpose, 

does not possess) another given relation, and on principle, 

the strength of these premises the conchision as- general 

serts that the presence (or absence) of one of the 

relations sometimes coincides with the presence (or absence) 

of the other— ^.^. .• 

Shakspeare was perfectly sane; 
Shakspeare was a genius; 
. • . Some geniuses (one at least) are perfectly sane, 
or Some perfectly sane persons are geniuses. 

Sin is evil; 
Sin exists; 
. • . Something evil exists. 

The ancient Stoics w^ere not enlightened by the Scrip- 
tures ; 
These Stoics believed in God ; 
. • . Some persons not enlightened by the Scriptures have 
believed in God. 

This figure is used mainly to disprove sweeping statements 
or alleged general law^s, by displaying cases to which they 
will not apply. If any one maintains that every genius is a 
morbid degenerate, we can disprove the statement by calling 

171 



172 THE THIRD FIGURE OF THE SYLLOGISM. 

his attention to the fact that Shakspeare or Goethe or Plato 
was a man of undoubted genius yet perfectly free from every 
trace of morbid degeneracy. If he maintains that in God's 
world no evil can exist, we need only point to sin. If he 
maintains that through the Scriptures alone can God be 
known, it is only necessary to remind him of tlie Stoics. 

In this figure more than in any other the machinery of the 
syllogism seems very cumbersome and unnecessary. In or- 
dinary speech and thought we consolidate the two premises 
into one statement : Shakspeare was a genius ^ and yet not 
morbid -^, Sin is an evil ^ and yet exists -^, The Stoics 
believed in God (j) (|) (j) , though not enlightened by the 
Scriptures -^ -^ -^. 

The PRINCIPLE on which we reason is evidently this : 

A single actual case in which two positive or negative relations 
coincide proves thai they are not incompatible. 

In the examples here given Shakspeare's freedom from 
morbidness and the Stoics' ignorance of the Scriptures may 
be regarded as negative relations. As applied to these two 
cases the principle means that freedom from morbidness is not 
inconsistent with genius, diXid vice versa; that ignorance of 
the Scriptures is not inconsistent with a knowledge of God, 
and vice versa. 

When both relations are negative a conclusion can be 
drawn quite as well as when one or both are positive. From 
the fact that stones are neither virtuous nor vicious -^ -^ -^ 
we can prove that the absence of one of these qualities does 
not necessarily preclude the absence of the other, and thus 
disprove the statement that everything in the world must be 
one or the other.* 

* The old syllogistic rule says : From tzvo negative premises no conctu- 
sion can be drawn; but in the third figure the rule is evaded by obverting 
one or both premises. So that if we say ' Stones aren't virtuous, and 
stones aren't vicious ' we cannot draw a conclusion, but if we say stones 
aren't virtuous and stones are not-vicious we can ! Conclusions do not 
depend upon the form of words in which the premises are stated, but 
upon the real state of affairs to which they point; yet when we consider 



PURPOSE, PRINCIPLE, AND GENERAL CAUTION. 173 

Our conclusion in the example given does not depend upon 
the mere fact that there are no such things as virtuous or 
vicious stones, for if there were no stones at all this would 
still be a fact, though the conclusion would not follow ; but 
upon the fact that there are stones which are neither virtuous 
nor vicious. To state the case more generally : The conclu- 
sion does not depend upon the fact that objects with the rela- 
tion in question do not exist, but upon the fact that objects do 
exist without the relation. 

This last statement suggests what is involved in the prin- 
ciple of the figure as I have stated it, but what cannot be too 
much emphasized, that the cases from which our conclusions 
are drawn must actually exist. We cannot prove that a good 
man may comiC to grief by Colonel Newcome, that a brave 
man may murder his wife by Othello, that good nature will 
.not save us from cruelty by Arthur Donnithorne, that wounds 
will not destroy existence by the heroes of Valhalla, or that 
a pumpkin-shell may be transformed into a chariot by the 
adventure of Cinderella. From particular cases in one uni- 
verse we cannot prove the compatibility of relations in 
another. 

The first caution to be observed in using this figure is 
— put technically — that its conclusion is always particular. If 
all men are mortal and all men are bipeds, we can be sure that 
so far as men are concerned these two attributes coincide, 
but this does not prove that every mortal creature has two 
legs or that angels and all other bipeds are sure to die. In 
other words, the fact thai certain objects possess each of several 
positive or negative relations does not prove that other objects may 
not possess 07ie without the other or exist without either. Or 
more briefly : 

7) Any number of coincidences between relations ivill not 
prove that they coincide always. 

this state of affairs there is a sense in which we can say that premises m 
this figure from which a conclusion can be drawn must both be affirma- 
tive in meaning, no matter what their form. See the next paragraph. 



174 THE THIRD FIGURE OF THE SYLLOGISM. 

The briefer statement is less comprehensive, but it will 
cover any case that is likely to arise.* 

In this figure as in the second we must be careful not to be 
confused by negative relations. From the fact that all M's 
are P, and that no M's are S, we can infer that 
rehi^ions. some P's are not S ; but we cannot infer that some 
S's are not P.f From the Pope we may perhaps 
prove that there are infallible mortals, but not that there are 
fallible immortals. It takes the Devil for that. The sixth 
caution or its corollary — ^^ Evidence sufficient to prove that 
some S's are not P's may not be sufficient to prove that some 
P's are not S's" — is one which we tend to ignore or mis- 
understand continually. Altogether the best way to observe it 
without confusion, whether we are reasoning in the third fig- 
ure or in one of the others, is to put our premises affirmatively, 
with the negative element, when there is one, in the predi^ 
cate {i.e., to obvert negative premises and conclusions). 
When we say that there are infallible mortals or that there 
are falHble immortals, our meaning is much clearer and the 
distinction between the two statements is much more obvious \ 

* This caution covers illicit minors in the third figure. Put in terms 

of causal relations the caution is this : 

A single coincidence proves the compatibility of relations, but no 

number of coincidences can prove their necessary connection. 

j This caution covers illicit majors in the third figure as well as in the 

second. 

if The statement in this form has moreover the advantage of directing 

attention to the fact that we are talking about real things. (See top of 

p. 173.) The diagrams in the text seem to me to accent the affirmative 

element which reasoning in the third figure 
particularly involves, as well as to guard 
against the confusion referred to in the text 
better than Euler's. Students always find 
it difficult to see why this figure does not 
mean that some P's are not S as well as that 
some S's are not P. But if we represent S 
by a vertical stroke and P by a horizontal 

the distinction between M which is S but not P -^ and M which is P 

but not S -^ is obvious, and with it the distinction between S not-P -4+ 

and P not-S -^. 




QUANTITY OF THE PREMISES. I7S 

than when we say that some mortals are not fallible or that 
some fallible beings are not mortal. 

By the coincidence of two relations we mean that they both 
belong to the same individual. Whether they do or not is 

primarily, of course, a matter of observation in 

, .1 1 1 1 • ' , Quantity 

each particular case : but when the coincidence of the 

premises, 
of the relations must be inferred by putting to- 
gether statements about the existence of each we must re- 
member one more caution : 

8) 7 wo different ?'elalwns can belong to individuals of the 
same class without belonging to the same individual, unless at 
least one of them belongs to every individual in the class,^^ 

If we know that this particular X is both Y and Z, we know 
of course that Y and Z coexist. If we know that every X is 
Y and every X is Z, we can be sure that each X is both Y 
and Z ; if we know that every X is Y and that some X is Z, 
we can be sure that some X or other is both Y and Z ; but 
if we only know that some X's or other are Y and that some 
X's or other are Z, we cannot be sure that Y and Z ever belong 
to the same X. This is what is meant in this figure by the 
technical rule that from two particular premises no conclusion 
can be drawn. The technical rule should have added that 
from a particular premise and a singular premise in the third 
figure no conclusion can be drawn ; for it does no good to 
know which particular X's are Y so long as we do not know 
which are Z. 

The principle and all the cautions can be put together in 
such a general statement as this : 

The coincidence of relations — whether positive or negative — 
proves that they are compatible, but it does not prove that either 
of them involves the other, or that the absence of one is co?7i- 
patible either with the presence or with the absentee of the other. 
Moreover the fact that two relations belong to objects of the same 
class will 7iot prove that they belo?ig to the same objects unless 
at least one of thein belongs to all the objects in the class. 
* This covers undistributed middles in the third fis:ure. 



CHAPTER XVI. 

THE ALLEGED FOURTH FIGURE.* 

So long as the various figures of the syllogism were dis- 
tinguished by the mere arrangement of terms rather than by 
the relations involved in the reasoning, it seemed 
of the reasonable that there should be a figure to repre- 

sent every possible arrangement. Consequently 
to the three figures which we have discussed, and which were 
all that Aristotle recognized, Galen (131-200 a.d.) added 
a fourth. The arrangement of terms in each is as follows: 
First Figure. Second Figure. Third Figure. Fourth Figure. 

MP PM MP PM 

SM SM MS MS 

SP SP SP SP 

The four figures cover every possible permutation of the 
terms. 

Reasoning in the fourth figure outside of exercises in 
formal logic is extremely rare. Beyond mere questions of 
whether one class includes or excludes members of another, 
Three ways it has no significance ; and though it is easy to 
with it. arrange problems in such a way that they will fall 

within the figure, they lose most of their meaning when so 
arranged and seem strained and unnatural. Nevertheless 
one ought to know how to deal with the problems when they 
arise. There are three ways of doing this. The first is to 
disregard their meaning and solve them by means of a set 
of purely mechanical rules. These rules are equally applica- 
ble to all four of the figures ; but inasmuch as we have tried 
* This chapter is not essential. 

176 



THREE WAYS OF DEALING WITH IT. l^^ 

to get along without them — or at least to interpret them — in 
the other figures, it seems a pity to take refuge in them now.* 
The second way of dealing with syllogisms in the fourth 
figure is to assume that they are concerned merely with rela- 
tions of inclusion or exclusion between a number of classes, 

all of which are assumed to exist, ^ --^ 

and then to test them by Euler's /^ y"""^ /a "^^^ 
diagrams. For example, / / / \ 

(S( M [ p 1 \ 

Some P's are M's ; 11 I / / 

All M's are S s ; \ \ \ J 
.*. Some S's are P's. \^^--^_^^ --'''' 

The conclusion follows ; for we cannot possibly put the circle 

M within the circle S, and part of _,. ,,, 

the circle P w^ithin the circle M, ^ -^'''' ^ <\. 

without some part of the area of / l\f \ 

S falling within the circle P. ( "^ ^ if ^ j 

Some P's are M's ; V \ / \ J 

No Ms are S's ; ^-- ^^ ^^ y 

.-. Some S's are not P's. ''^ '"'' 

* The rules, as stated by Jevons, are as follows : 

1. Every syllogism has three and only three terms. These terms are 
called the major term, the minor term, and the middle term. 

2. Every syllogism contains three and only three propositions. These 
propositions are called the major premise, the minor premise, and the 
conclusion. 

3. The middle term must be distributed once at least, and must not be 
ambiguous. 

4. No term must be distributed in the conclusion w^hich was not dis- 
tributed in one of the premises. 

5. From negative premises nothing can be inferred. 

6. If one premise be negative, the conclusion must be negative ; and 
vice versa, to prove a negative conclusion one of the premises must be 
negative. 

From the above rules may be deduced two subordinate rules, which it 
will nevertheless be convenient to state at once. 

7. From two particular premises no conclusion can be drawn. 

8. If one premise be particular the conclusion must be particular. 

These rules are not absolutely reliable unless we assume that the 
objects denoted by each term in the syllogism exist. 



lyS THE ALLEGED FOURTH FIGURE. 

The conclusion does not follow, for we can construct a 
diagram which represents the premises without representing 
the supposed conclusion. 

The third, and of course the best, way of dealing with 
syllogisms in the fourth figure which we are called upon to 
test is to try to give them a rational interpretation and thus 
work in the light. When we come to interpret such syl- 
logisms we shall find that we must regard them as concerned 
either with the relations between classes which we have just 
discussed or with the relations peculiar to some one of the 
three other figures, to which the syllogism in question cai. be 
' reduced ' by converting the conclusion or one or both of 
the premises. 

If we turn back to the table which shows the arrangement 
of terms in each figure, it is easy to see that by converting 
the major premise of a syllogism in the fourth figure we 
Formal S^^ ^^^ arrangement of terms found in the third ; 

reduction. ^y converting the minor we get that found in the 
second ; and by converting the conclusion or by converting 
both premises we get that found in the first. It is thus 
formally possible to interpret the fourth figure by any one 
of the three others ; and so long as we do not attempt to 
test a universal conclusion by the third figure (which is 
itself incapable of giving such a conclusion) or an afiirmative 
conclusion by the second (which never gives it), that is to 
say, so long as we do not ask a figure to test a kind of con- 
clusion that it is itself unable to draw, it does not make the 
slightest difference, as far as the formal process is concerned, 
which of the first three figures we use to test a syllogism in 
the fourth. If it is valid, there are always at least two of 
the first three figures in which the conclusion can be proved. 
But since the second and the third figures both have the 
limitations just referred to, any one who merely wants an 
easy formal test will save himself some thinking by making 
it a rule to test every argument in the fourth figure by re- 
ducing it to the first. In doing this he may assume that 



FORMAL REDUCTION. 179 

no syllogism in the fourth figure is valid unless the conclu- 
sion can be obtained either by converting a conclusion which 
can be drawn in the first figure from the same premises, or 
by reasoning in the first figure from the converse of the 
premises. In other words, if you have to test a syllogism in 
the fourth figure, ask first whether it is not merely a syl- 
logism in the first figure with the conclusion converted (or 
converted and weakened, i.e., O from E as well as I from A). 
If it is, the reasoning is usually assumed to be valid. If it is 
not, then convert the premises, if they can be converted 
(remembering that A must be converted into I and that O 
cannot be converted at all), and see whether the conclusion 
in question will not follow from them according to the prin- 
ciple of the first figure without the violation of any caution. 
If it will, the syllogism in the fourth figure is assumed to be 
^^alid ; but if the syllogism will not stand either of these tests, 
it certainly is not valid. 

Here are some examples : 

(i) All P'sare M's ; 
All M's are S's ; 

. • . Some S's are P's. 

According to the rule just laid dow^n this syllogism is valid, 
because from the premises as they stand we can reason in the 
first figure to the conclusion ^ All P's are S's', which by 
conversion gives the conclusion in question ' Some S's are 
Fs'. 

The following syllogism is not valid: 

(2) All P's are M's; 
All M's are S's; 

.-. All S's are P's; 

because (i) the universal conclusion is more than we can get 
by converting '*■ All P's are S's ", and (2) if we convert the 
premises we get 

Some M's are P's; 

Some S's are M^s : 



i8o THE ALLEGED FOURTH FIGURE. 

from which we cannot draw any conclusion whatever without 
disregarding the caution which says that from a statement 
about some undesignated members of a class we cannot infer 
anything about any designated member or any one of a desig- 
nated set of members. 

(3) No gods are Americans ; 
All Americans are mortal ; 

. • . Some mortals are not gods. 

To reduce this syllogism to the first figure we must convert 
the premises, e.g., 

No Americans are gods ; 
Some mortals are Americans ; 
. • . Some mortals are not gods. 

This reasoning is perfectly valid, and thus our original syl- 
logism is vindicated. 
One more example : 

(4) All students are human ; 

No human beings like torture ; 

. • . Some beings that like torture are not students. 

This syllogism can be proved valid like the others by means 
of the first figure, though when we try to ' reduce ' it a diffi- 
culty immediately confronts us, for the conclusion of the 
syllogism is a particular negative proposition which cannot 
be converted, and when we convert the premises the con- 
clusion will not follow, viz. : 

Some human beings are students ; 

No beings that like torture are human ; 

. • . Some beings that like torture are not students. 

To reason in this way violates this caution : ' To say that 
something is true of certain objects does not imply that it is 
false of others', i.e., to say that some (or all) human beings 
are students does not imply that beings who like torture and 
are therefore not human are not students. 

We cannot convert the conclusion, we cannot prove it by 
converting the premises, and yet the reasoning is valid ! I 



FORMAL REDUCTION. l8l 

gave this example in order to bring out the difference between 
converting a conclusion and obtaining that conclusion by 
converting something else. P>om the premises in question, 

* No human beings like torture ' and ' All students are 
human', we can reason in the first figure to the conclusion 
that ' No students like torture '. Converting this we get 

* No beings that like torture are students \ and if this is true 
it is necessarily true also that ' Some beings that like torture 
are not students ' . The fact that this is less (if it really is less) 
than we might have inferred does not interfere with the valid- 
ity of the inference. That is to say, the conclusion given in 
the example can be obtained by converting the conclusion in 
the first figure, though the conclusion in the first figure can- 
not be obtained by converting the conclusion given in the 
example. We were testing the fourth figure by the first, not 
the first by the fourth ! 

I have spoken at some length about this reduction to the 
first figure because it is the traditional method of testing syl- 
logisms not only in the fourth figure but in the second and 
third as well. But an undiscriminating reduction to the first 
figure has no more value for thought than a mechanical use of 
cut-and-dried ' rules of the syllogism ', and probably has much 
less value than the use of the diagrams. Our thought grows 
mechanical all too soon, and it is a pity for logic of all studies 
to hasten the process. If we are really to work in the light 
in testing syllogisms of the fourth figure, their ' reduction ' 
must be accompanied by their interpretation, and the figure 
to which we reduce them must be determined by the inter- 
pretation — not by mere convenience for formal manipula- 
tion.^ 

* Looking back at example No. i, let us fill it out as follows : 

All persons a hundred miles above the surface of the earth (P's) are 
organic beings beyond the pressure of the atmosphere (M's). 

All organic beings beyond the pressure of the atmosphere (M's) become 
greatly swollen (S's). 

From these premises it is easy enough to draw the conclusion in the 
first figure that all persons a hundred miles above the surface of the earth 



l82 THE ALLEGED FOURTH FIGURE. 

(P's) become greatly swollen (S); meaning that if a person should reach 
such an altitude the intra-organic pressures, not counteracted by pres- 
sure from without, would cause him to swell up. But the conclusion in 
the fourth figure, that some things which become greatly swollen (S's) 
are persons a hundred miles above the surface of the earth (P), looks 
more like a description of some actually existing swollen objects than 
like an account of what would happen under certain purely hypothetical 
circumstances. It cannot be turned into hypothetical form, and the im- 
plication that such things as swollen persons a hundred miles above the 
surface of the earth exist is certainly much stronger, to say the least, 
than in the conclusion drawn according to the first figure. In so far as 
it involves such an implication the conclusion in the fourth figure is of 
course misleading and fallacious, for we have no right to confuse hypo- 
thetical and real conditions. (See page 109, note.) 

Example No. 3 can be reduced as we have seen to the first figure, but 
if the two universal propositions which compose the premises are inter- 
preted as stating causal relations no conclusion is possible; that is to say, 
from the fact that deity involves not being an American and that being 
an American involves mortality we cannot draw any conclusion. The 
conclusion follows only if we assume that Americans exist. It is in the 
third figure that the syllogism is most natural and most significant, e.g,: 
All Americans are mortal and none of them are gods; therefore ' Some 
mortals are not gods '. The Americans, not gods or mortals as such, are 
evidently the concrete individuals from a knowledge of whom the con- 
clusion is drawn. 

In the case of example No. 4 the conclusion drawn, " Some beings that 
like torture are not students ", stands the traditional test of reduction to — 
or rather deduction from — the first figure; but so far as it implies that 
beings who like torture exist, it does not follow from the premises. Even 
the universal conclusion, '' No beings that like torture are students ", 
is likely to be misleading, because the causal relation between being a 
student and disliking torture is so remote that the statement looks a good 
deal like a description of actually existing beings that like torture. It 
would have been better to say that if any being likes torture it is not 
a student. It is this which follows from the premises. 

The sum and substance then of what I have said in criticism of this 
figure is this: It obscures the real relations under discussion, and in doing 
so is likely to lead to erroneous conclusions besides tempting us to 
work in the dark by a rule of thumb. 



CHAPTER XVII. 
OTHER DEDUCTIVE ARGUMENTS. 

We have already distinguished between categorical propo- 
sitions and those which are hypothetical or dis- 
junctive. The syllogisms discussed so far S^iog^gm^g^^^ 
involved only categorical propositions, but there 
are also syllogisms in which hypotheticals and disjunctives 
have a place. 

Hypothetical syllogisms run as follows: 

If A is B, C is D; If a- man is a Christian, he forgives; 
A is B; J. S. is a Christian; 

. • . C is D. . • . J. S. forgives. 

If A is B, C is D; If a man is a Christian, he forgives; 
C is not D; J. S. does not forgive; 

. • . A is not B. . • . J. S, is not a Christian. 

A Hypothetical Syllogism is thus one in which the major 
premise is a hypothetical proposition and the minor a cate- 
gorical. 

The first pair of examples, in which the state of affairs 
mentioned in the consequent part of the major premise is 
proved to exist, are said to be constructive or of the inodus 
ponens; the second pair, in which the state of affairs men- 
tioned in the antecedent part of the major is proved not to 
exist, are said to be destructive or of the 77iodus tollens. 
According to this a syllogism might be constructive though 

183 



1 84 OTHER DEDUCTIVE ARGUMENTS. 

its conclusion were negative, and destructive though affirma- 
tive, e.g.: 

If A is B, C is not D; 

AisB; 
. • . C is not D (Constructive). 

If A is not B, C is not D; 
Cis D; 
.•. A is B (Destructive). 

Hypothetical syllogisms look like an entirely new sort; 
but the novelty lies altogether in the verbal form, not in the 
relations expressed; for we have seen (page 109) that the 
relations expressed by hypothetical propositions can be 
expressed about as well in universal categorical propositions, 
and when the hypothetical major premise of a hypothetical 
syllogism is put into categorical form only a slight change 
is required in the minor to make the syllogism also cate- 
gorical. Making these changes, we get 

A state of affairs in which A is B is a state of affairs 

in which C is D; 
This is a state of affairs in which A is B; 
. • . This is a state of affairs in which C is D. 
A Christian forgives; 
J. S. is a Christian; 
. • . J. S. forgives. 

A state of affairs in which A is B is a state of affairs in 

which C is D; 
This is a state of affairs in which C is not D; 
.• . This is a state of affairs in which A is not B. 
A Christian forgives; 
J. S. does not forgive; 
. • . J. S. is not a Christian. 

The constructive hypothetical syllogism thus resolves itself 
into an ordinary syllogism in the first figure; the destructive 
into one in the second. 

The formal rule for hypothetical syllogisms is that ilhe 



HYPOTHETICAL SYLLOGISMS. 185 

minor premise must either affirm the antecedent of the hypo- 
thetical proposition in the major (as in the first two of these 
last examples) or deny the consequent (as in the second two). 
In the first of the following examples we commit the Fallacy 
of Denying the Antecedent; in the second, the Fallacy of 
Affirming the Consequent, 

If a man is a Christian, he forgives; 
j. S. is not a Christian; 
. • . J. S. does not forgive. 

If a man is a Christian, he forgives; 
J. S. forgives; 
. • . J. S. is a Christian. 

Turning from words to things, the meaning of the formal 
rule is as follows: 

If the presence of one state of affairs (AB) ahvays involves 
the presence of another (CD), and if the first state of affairs 
(AB) is present, the second state of affairs (CD) must also be 
present; if the second state of affairs (CD) is absent, the first 
state of affairs (AB) cannot be there to involve its presence; 
but the first state of affairs (AB) can be absent without 
involving the absence of the second (CD); and the second 
(CD) can be present without involving the presence of the 
first (AB). 

These fallacies of * denying the antecedent ' and ' affirming 
the consequent ' would not be fallacies at all if the world 
were so constituted that there was only one cause capable 
of producing a given effect or one premise capable of involv- 
ing a given conclusion. If a person had to be drowned in 
order to be killed, we could not only say, ' He is drowned, 
therefore he is killed ', ' He is not killed, therefore he is not 
drowned ' ; but we could also say, ' He is not drowned, 
therefore he is not killed ', and * He is killed, therefore he is 
drowned \ To avoid the fallacy we should think of what 
we are saying and remember that the world is not consti- 
tuted in this way, but that any one of several causes may pio- 



l86 OTHER DEDUCTIVE ARGUMENTS. 

duce essentially the same result and any one of several prem- 
ises involve the same conclusion. 

Disjunctive Disjunctive Syllogisms are those which con- 
syllogisms, tain a disjunctive major premise and a categorical 
minor, e.g. : 

A is either B or C; Either J is not K or L is M; 
A is not B; J is K; 

. • . A is C. .-. L is M. 

In order that any conclusion should be justified it is 
necessary that the minor premise deny the existence of one 
of the alternatives mentioned in the major. We cannot say 
'A is either B or C; it is B; therefore it is not C '.* 

What we must be most careful about in the case of these 
syllogisms is to see that the major premise is really true; 
that there is no alternative which it does not mention. We 
should not say 'This man must be either wise or foolish, he 
is not wise, therefore he is foolish' ; for there are many per- 
sons of medium intelligence who cannot fairly be called 
either wise or foolish. 

A Dilemma is ' a syllogism having a hypothetical major 
premise with more than one antecedent and a disjunctive 
minor'. '* In common speech ... we are said 
to be in a dilemma when we have only two 
courses open to us and both of them are attended by 
unpleasant consequences. In arguments we are in this 
position when we are shut into a choice between two admis- 
sions and either admission leads to a conclusion which we 
do not like." f 

According to Jevons the Dilemma takes at least three 
different forms. ' ' The first form is called the Simple Con- 
striictive Dilenujia: 

If A is B, C is D; and if E is F, C is D; 
But either A is B, or E is F; 
Therefore C is D. 

* See p. io6 on meaning of ' either '. \ Minto, p. 222. 



DILEMMAS. 187 

'* Thus ' if a science furnishes useful facts, it is worthy of 
being cultivated; and if the study of it exercises the reason- 
ing powers, it is worthy of being cultivated; but either a 
science famishes useful facts, or its study exercises the 
reasoning powers; therefore it is worthy of being cultivated. ' 

" The second form of dilemma is the Complex Consiruciive 
Dilemma^ which is as follows: 

If A is B, C is D; and if E is F, G is H; 
But either A is B, or E is F; 
Therefore either C is D, or G is H. 

** It is called complex because the conclusion is in the 
disjunctive form. As an instance we may take the argu- 
ment, * If a statesman who sees his former opinions to be 
wrong does not alter his course, he is guilty of deceit; and 
if he does alter his course, he is open to a charge of incon- 
sistency; but either he does not alter his course or he does; 
therefore he is either guilty of deceit or open to a charge of 
inconsistency. ' In this case as in the greater number of 
dilemmas the terms A, B, C, D, etc., are not different.'' 

The third form — the Destructive Dilemma — ' ' is always com- 
plex, because it could otherwise be resolved into two uncon- 
nected destructive hypothetical syllogisms. It is in the 
following form : 

If A is B, C is D; and if E is F, G is H; 
But either C is not D, or G is not H ; 
Therefore either A is not B, or E is not F. 

*' For instance, ' If this man were wise, he would not speak 
irreverently of Scripture in jest; and if he were good, he 
would not do so in earnest; but he does it either m jest or 
in earnest; therefore he is either not wise or not good' 
(Whately). 

" Dilemmatic arguments are, however, more often fal- 
lacious than not, because it is seldom possible to find 
instances where two alternatives exhaust all the possible 



1 88 OTHER DEDUCTIVE ARGUMENTS. 

cases, unless indeed one of them be the simple negative of 
the other in accordance with the law of excluded middle. 
Thus if we were to argue that ' if a pupil is fond of learning 
he needs no stimulus, and that if he dislikes learning no 
stimulus will be of any avail, but that, as he is either fond of 
learning or dislikes it, a stimulus is either needless or of no 
avail ', we evidently assume improperly the disjunctive minor 
premise. Fondness and dislike are not the only two possi- 
ble alternatives, for there may be some who are neither fond 
of learning nor dislike it, and to these a stimulus in the 
shape of rewards may be desirable." * 

Principles of logic have reference to the relations of 
objects, not to the words in which those relations are 
expressed. From this it follows that variations 
forms of can be introduced into the wording of an argu- 

argument!^ ment without affecting its validity. One varia- 
tion that has seemed important enough to be 
discussed in almost every text-book since Aristotle consists 
in taking for granted certain of the relations involved, 
without any explicit mention of them. ' Enthymemes ', 
* Epicheiremata ' and ' Sorites ' are names for arguments 
abridged in different ways. 

An Enthymeme (from ev, in, and dvfAO^, the mind) is a 
syllogism — usually categorical — in which one of the premises 
or the conclusion is not expressed. 

Supposing the syllogism in question to be this: 

All men are mortal; 
Socrates is a man; 
Therefore Socrates is mortal ; 

our reasoning would have been almost as clear and more 
effective rhetorically if we had merely said : 

(7) Socrates is a man, 

Therefore he is mortal ; 

^ " Lessons in Logic ", p. 167. 



THREE FORMS OF ABBREVIATED ARGUMENT. 189 

or (2) All men arc mortal, 

Therefore Socrates is mortal; 
or (j) All men are mortal, 

And Socrates is a man.* 

Reasoning often takes the form of a chain in which the 
'conclusion of one syllogism is used as one of the premises 
of another, e.g. : 

All A's are B's; 
All B'sareC's; 
Therefore all A's are C's. 

All A'sareC's; 
All C's are D's; 
Therefore all A's are D's. 

The syllogism which supplies such a premise is called a 
Prosyllogisvi; that which uses it, an Episyllogism, 

When an Episyllogism depends upon a Prosyllogism which 
is only partly expressed the argument is called an Epichei- 
renia, e.g. : 

All A's are C's, for they are B's; 
All C's are D's, for they are X's; 
Therefore all A's are D's. 

This is " a double Epicheirema, containing reasons for 
both premises ". 

A Sorites is a chain of prosyllogisms and episyllogisms in 
which all the conclusions but the last are unexpressed, e.g.: 

All A's are B's; All Athenians are Greeks; 

All B's are C's; All Greeks are men; 

All C's are D's; All men are mortal; 

All D's are E's; All mortals fear; 

Therefore all A's are E's. . • . All Athenians fear. 

* Where the major premise is omitted the enthymeme is said to be of 
the first order ; where the minor, of the second ; where the conclusion, of 
the third. 



190 OTHER DEDUCTIVE ARGUMENTS. 

If we put in the suppressed conclusions, the Sorites is 
resolved into these syllogisms: 

All A's are B's; All B's are C's; . • . All A's are C's. 

All A's are C's; All C's are D's; . • . All A's are D's. 

All A's are D's; All D's are E's; . • . All A's are E's. 

With reference to a Sorites it should be observed : 

i) That almost invariably the minor premise of each 

syllogism involved is written first. A Sorites which begins 

at the other end seems jagged. 

2) That in any valid Sorites every premise but the first 
(/.^., the minor premise of the first prosy llogism^) must be 
universal and every premise but the last {i,e., the major 
premise of the last episyllogism) affirmative. 

3) That while the last syllogism involved (the episyllo- 
gism) may be in any figure, each prosyllogism must be in 
the first; and that in the case of each prosyllogism it is the 
minor premise which the previous prosyllogism supports. 



CHAPTER XVIII. 
BLUNDERS IN WORD AND BLUNDERS IN THOUGHT. 

Fallacies or blunders in reasoning are usually divided 
into two great classes: ' Logical ' or ' Formal ' [Fallacice in 
dictione) and ' Non-logical ' or ' Material ' [FallacicB extra 
diciionem or in re). V/hen logic is regarded as a science of 
the ' forms of thought ' or the science which treats of the 
proper arrangement of words in correct thinking (on the 
assumption that the ' forms ' of thought and the forms or 
arrangements of words correspond) this distinction presents 
no difficulties: logical or formal fallacies are those which 
result from a violation of the rules which logic lays down for 
correct thinking and the corresponding arrangement of 
words; and material or non-logical fallacies are those which 
occur in spite of the observance of these rules — they do not 
depend upon the general laws of thought or arrangement of 
words at all, and can only be avoided by a knowledge of the 
matter thought about. 

In the foregoing pages I hope it has been made plain that 
the same arrangement or form of words cannot be counted 
upon to always express the same thought. I hope it has 
been made plain too that the so-called ' laws ' and ' forms ' 
of thought with which it is often said that logic deals have 
no meaning whatever apart from the things thought about 
and the way in which the relations of these things involve 
each other. If these views are correct it is quite impossible 
to make any fundamental distinction between fallacies which 

191 



192 BLUNDERS IN WORD AND IN THOUGHT. 

are due to some perversion of the forms of thought and those 
which are due to some mistake about the relations of things. 
But we might still distinguish between fallacies which are 
due to some misconception about the ' matter ' under dis- 
cussion and those which depend in some way upon the 
' form ' of words used in discussing it. So with the terms 
* logical ' and ' extra-logical \ They may be taken to mean 
that some fallacies result from a violation of logic while 
others do not, or they may be taken to mean that some are, 
and others are not, concerned with /ogoi or words. 

Now it is true that logic has not made such elaborate 
provision against every fallacy possible as it makes against 
those already discussed, and yet fallacious thinking is always 
illogical and there is no reason but one of convenience why 
books on logic should discuss some and not others. It is 
not appropriate therefore to divide fallacies into those that 
violate the rules of logic and those that do not. But there 
is a reason why we should divide fallacies into those that 
result in some way from the improper use of words and those 
that do not. We may therefore accept this division into 
' logical ' and ' extra-logical ' or ' material ' on the under- 
standing that it is equivalent to a division into blunders that 
result mainly from the careless use of words and those that 
do not. 

The * logical ' fallacies are usually subdivided into two 
classes called ' Purely logical ', " where the fallaciousness 
is apparent from the mere form of expression ", and ' Semi- 
logical \ where the fallaciousness is not apparent from the 
mere form of expression but is due to some ambiguity in the 
language used or some misunderstanding as to its meaning. 
Of the ' semi-logical ' fallacies we shall have nothing more 
to say. We have seen already how insidious they are, why 
they arise, and how best to guard agamst them. 

With the ' purely logical ' fallacies we are also familiar. 
They are such blunders as we make when we ignore the 
cautions of the syllogism, or convert A simply or O at all, or 



j 



'PURELY LOGICAL.' 193 

reason that because all S is P all non-S is non-P, or infer 
the falsity of a consequent from the falsity of 
Its antecedent, or the truth of the antecedent J^^^ai/ 
from the truth of the consequent, or the falsity 
of a conclusion from the falsity of the premises, or the truth 
of the premises from the truth of the conclusion. In all 
such cases it is ' apparent from the mere form of expres- 
sion ' that the reasoning is inconclusive; the blunder can 
be detected without inquiring into the truth of the premises 
or even into the meaning of the terms; so that a purely 
logical fallacy, unlike any of the others, can be detected 
when the terms are mere unmeaning words or symbols such 
as S, M and P, or X, Y and Z. 

The strange thing about these so-called purely logical 
fallacies is that they are committed so often. How is it 
possible, we may ask, to think so badly ? If the reader will 
ask the following questions to some unsuspecting person and 
does not allow very much time to elapse between the 
answering of one and the asking of the next, the result of 
the experiment may help to make the matter clear: 
Who was the first man ? 
Who was the first woman ? 
Who killed Cain ? 

Abel did not kill Cain, but his name will usually be men- 
tioned, or at least come to mind, merely because it comes 
naturally at the end of the series ' Adam, Eve, Cain ' and 
fits into the atmosphere of murder. It is largely a mere 
matter of the verbal jingle, the answer resulting from the 
same law of habit in the nervous system that accounts for 
putting one's pen in the paste-pot after using the brush. 
Most of these so-called purely logical fallacies come in pre- 
cisely the same way. Inference is in the air and the jingle 
seems to fit, so we spurt out something when the premises 
will not justify any inference whatever, or an ' All ' or a 
' No ' that fits the jingle when the premises justify only a 
* Some '. If we say: 



194 BLUNDERS IN WORD AND IN THOUGHT. 

AllXisY; 
. AllYisZ; 
. • . All X is Z, 

the reasoning is valid, but if we say: 

No X is Y; ) or No X is Y; 

No Y is Z; [ All Y is Z; 

.-. No XisZ; ) .-. NoXisZ, 

it is not valid though we have merely substituted * No ' for 
' Air or ' No X ' for ' All X ' throughout, without affecting 
the jingle. Indeed if we had only said ' No-X ' instead of 
' No X ' the reasoning in the last case would have been 
precisely similar to that in the first and just as valid. Again 
if we say 

Five francs are a dollar; 
Four shillings are a dollar; 
. • . Five francs are four shillings, 

the inference is perfectly valid; but if we say in precisely 
similar form 

Blades of grass are green; 
Frogs are green ; 
. • . Blades of grass are frogs, 

the inference is not valid. The reason is, of course, that 
the copula ' are ' is used in different senses in the two 
syllogisms; but when we do not stop to think of the sense, 
the familiar jingle, assisted perhaps in this case by some 
recollection of Euclid's axiom that ' things equal to the same 
thmg are equal to each other ', lures us on to danger. 

In spite of a real confusion of meaning sometimes asso- 
ciated with some of these ' purely logical fallacies ', they can 
hardly be called the result of bad thinking; because they are 
not the result of thinking at all, but only of a reflex act. 
On this account it might have been more appropriate to call 
them the Reflex Fallacies or the Jingle Fallacies. 

As there are two classes of verbal fallacies, so also there 



TWO KINDS OF MATERIAL FALLACIES. I95 

are two classes of the material or non-verbal fallacies, which 

may be called respectively Fallacies of the For- 

T 1 T- II • r 1 Til 1 Two kinds 

gotten issue and Fallacies 01 the ill-conceived of material 

Universe. Fallacies of the Forgotten Issue are 
not particularly characteristic of deduction; but some of 
them are usually discussed in connection with it, and there- 
fore we shall speak of them in the next chapter. In the 
chapter after that we shall discuss Fallacies of the Ill-con- 
ceived Universe. These do not belong to the traditional 
field of deduction, because there are no rules for verbal 
manipulation which they break. Yet I have tried to show 
that all deductive inference depends upon the assumption 
that things have certain general relations, and that deductive 
fallacies occur when these relations are overlooked; and if 
this is correct these fallacies of the Ill-conceived Universe 
are essentially similar to the fallacies of deduction in their 
ultimate nature, though they may not be caused like them 
by a verbal jingle. 

Nothing has been said in the foregoing pages about the 
fallacy known as ' Non Sequitur '. This name is really 
applicable, as the words imply, to every argument 
in which the conclusion does not follow, and in Seguitur. 
this sense of the words every fallacy is a Non Sequitur. 
But the phrase is often applied in a more restricted sense to 
those arguments only in which the conclusion does not even 
appear to follow, except perhaps to the most hasty and 
careless of reasoners; as in the following examples: The 
earth is round; therefore there is no atmosphere on the 
moon. " Every one desires happiness, and virtuous people 
are happy, therefore every one desires to be virtuous." 
" Episcopacy is of Scripture origin, the Church of England 
is the only established church in England; ergo the church 
established is the church that should be supported." The 
subject requires no further consideration. 



CHAPTER XIX. 
THE FORGOTTEN ISSUE. 

A Fallacy of the Forgotten Issue is committed when we 
forget what it was that an argument was intended to prove, 
and either take that very thing or something equivalent to it 
and quite as doubtful for granted, or else prove something 
which is not equivalent to the point at issue and then assume 
that we have proved the point itself. In the first case the 
fallacy is called Petitio Principii or Begging the Question. 
In the second it is called Ignoratio Elenchi or a fallacy of 
Irrelevance. Each of these two fallacies of the forgotten 
issue takes several forms. 

The fallacy of Petitio Principii is not committed unless 
there is a show of proof. Nobody commits it who merely 
Petitio ^^y^ ' ^ assume these conclusions to be true, and 

Principii. j (Jq j^q|- ^j-y ^q prove them'. But a person does 
commit it if he thinks he is proving his conclusions when 
he is really assuming them, or is assuming a premise that is 
not admitted or would not be admitted if its real significance 
were understood. Often the premise is actually proved from 
the conclusion, or ' is such as would naturally and properly 
be so proved '. But in any case in which the fallacy is 
present the conclusion seems to be more fully proved by the 
argument than it really is, because it is not clearly understood 
how nearly equivalent is that which is taken for granted to 
that which is to be proved; e.g., "Whoever refuses to 
believe in the inspiration of the Bible makes the Most High 

196 



PETITIO PRINCIPII. 197 

a deceiver; for has he not told us that ' All scripture is given 
by inspiration of God ' V Of course we have no reason to 
believe that it was really God who said that all scripture is 
given by his inspiration unless we already assume that the 
Bible or some part of it is inspired. 

Whately directs attention to the fact that the English 
language is peculiarly " suitable for the fallacy of Petitio 
Principii, from its being formed from two distinct languages, 
and thus abounding in synonymous expressions which have 
no resemblance in sound, and no connection in etymology; 
so that a Sophist may bring forth a proposition expressed in 
words of Saxon origin, and give as a reason for it the very 
same proposition stated in words of Norman origin; e.g., 
' To allow every man an unbounded freedom of speech must 
always be, on the whole, advantageous to the State; for it 
is highly conducive to the interests of the community, that 
each individual should enjoy a liberty perfectly unlimited 
of expressing his sentiments ' ". 

A blunder of this same sort is committed when a student 
says that two chemicals are sure to unite since they /lave an 
affinity for each other; or that he knows unsupported objects 
will fall to the earth, from the fact that they are attracted 
towards it. 

'' Connected w^th this fallacy is the rhetorical device 
[already discussed] of Question-begging Epithets. Thus, 
though the matter we are discussing is open to dispute, we 
may speak of a nefarious project, a laudable am- includes 
bition, an astute act, a far-sighted policy, and epithets. 
so on, attempting, by means of a carefully selected epithet, 
to assume the point at issue, or at least to create an unfair 
prejudice in the mind of the hearer or reader whom we ad- 
dress/' ^ 

When a conclusion is based upon a premise which in an 
earlier stage of the argument was itself based 
upon this very conclusion, the reasoning is said ^ ^ ^ ®' 
* Fowler's '' Deductive Logic" (Clarendon Press). 



19^ THE FORGOTTEN ISSUE, 

to be in a Circle (Cir cuius in Probando), Here are some 
examples : 

First Syllogism. Second Syllogism. 

A is B; A is C; 

BisC; CisB; 

. • . A is C. . • . A is B. 

** Some mechanicians attempt to prove (what they ought 
to lay down as a probable but doubtful hypothesis) that 
every particle of matter gravitates equally; ' why .? ' because 
those bodies which contain more particles ever gravitate 
more strongly, i.e., are heavier: * but (it may be urged) those 
which are heaviest are not always more bulky; ' ' no, but 
still they contain more particles, though more closely con- 
densed ; ' ' how do you know that .? ' ' because they are 
heavier; ' ' how does that prove it ? ' ' because all particles 
of matter gravitating equally, that mass which is specifically 
the heavier must needs have the more of them in the same 
space'" (^Whately). 'Any man who would marry such a 
woman must have something wrong with him. ' ' Why, 
what is the matter with his wife V 'It is matter enough to 
be willing to marry such a man as he is.' 

If there are a large number of intermediate steps and the 
argument is a long one it may be very difficult to detect the 
circle. This fallacy, like a good many others, can be best 
guarded against by making the shortest and simplest possible 
summary of any argument that claims our interest. 

Ignoratio Elenchi or Irrelevance, the other fallacy of the 
forgotten issue, consists merely in arguing beside the point. 
" I am required by the circumstances of the case (no matter 
lenoratio why) to prove a certain conclusion; I prove, 
Elenchi. ^^^ that, but one which is likely to be mistaken 

for it; — in this lies the fallacy. . . . For instance, in- 
stead of proving that ' this prisoner has committed an 
atrocious fraud \ you prove that ' the fraud he is accused of 
is atrocious'; instead of proving, as in the well-known tale 
of Cyrus and the two coats, that ' the taller boy had a right 



IGNORATIO ELENCl II. 199 

to force the other boy to exchange coats with him ', you 
prove that ' the exchange would have been advantageous to 
both '; instead of proving that ' a man has not a right to 
educate his children or dispose of his property in the way he 
thinks best\ you show that ' the way in which he educates his 
children or disposes of his property is not really the best'; 
instead of proving that ' the poor ought to be relieved in this 
way', you prove that 'they ought to he relieved', ... A 
good instance of the employment and exposure of this fallacy 
occurs in Thacydides, in the speeches of Cleon and Diodotus 
concerning the Mitylenaeans : the former (over and above his 
appeal to the angry passions of his audience) urges \h^ justice 
of putting the revolters to death; which, as the latter 
remarked, was nothing to the purpose, since the Athenians 
were not sitting in Judgment, but in deliberatio7i, of which the 
proper end is expedie7icy. ' ' * 

It is interesting to find counterparts of this story in the 
history of our own times. The following sentences from 
Bismarck's Autobiography (Chapter XX) refer to the Austrian 
proposals for peace after the Prussian victories in the war of 
1866: 

*' I unfolded to the King [of Prussia] the political and 
military reasons which opposed the continuation of the war. 

'' We had to avoid wounding Austria too severely; we had 
to avoid leaving behind in her any unnecessary bitterness of 
feeling or desire for revenge; we ought rather to reserve the 
possibility of becoming friends again with our adversary of 
the moment, and in any case to regard the Austrian state as 
a piece on the European chess-board and the renewal of 
friendly relations with her as a move open to us. If Austria 
were severely injured, she would become the ally of France 
and of every other opponent of ours; she would even sacrifice 
her anti-Russian interests for the sake of revenge on 
Prussia. ... 

* Whately, '' Elements of Logic ", third edition, London, 1829. 



200 THE FORGOTTEN ISSUE. 

"To all this the King raised no objection, but declared 
the actual terms as inadequate, without, however, definitely 
formulating his own demands. Only so much was clear, 
that his claims had grown considerably since July 4. He 
said that the chief culprit [Austria] should not be allowed 
to escape unpunished, and that justice once satisfied, we 
could let the misled backsliders [the smaller German states 
that had sided with Austria] off more easily, and he insisted 
on the sessions of territory from Austria which I have already 
mentioned. I replied that we were not there to sit in judg- 
ment, but to pursue the German policy. Austria's conflict 
in rivalry with us was no more culpable than ours with her; 
our task was the establishment or initiation of a German natiofial 
unity under the leadership of the King of Prussia, 

"Passing on to German states, he spoke of various 
acquisitions by cutting down the territories of our opponents. 
I repeated that we were not there to administer retributive 
justice, but to pursue a policy; that I wished to avoid in 
the German federation of the future the sight of mutilated 
territories, whose princes and peoples might very easily 
(such is human weakness) retain a lively wish to recover 
their former possessions by means of foreign help; such allies 
would be very unreliable/' ^ 

" So Canning, in a speech in the House of Commons in 
reply to Mr. Percival, says: * The question is not, as assumed 
by my opponent, whether we shall continue the war in the 
Peninsula, but whether it is essential to our success in the 
war that our present system of currency remain unchanged. ' 
Thus it is not unusual, after a protracted debate, for the 
cooler thinkers to preface their remarks with reminding the 
audience of the real nature of the point on which issue is 
joined; and the longer and more heated the discussion, the 
greater the need for these monitory exordiums. For, 
especially when the field of debate is large, the combatants 

* *< Bismarck the Man and the Statesman". (Harper & Bros., 1899.) 



INCLUDED 'AD IIOMINEM' 20l 

often join issue on the wrong points, or do not join issue at 
all. One goes to the east, another to the west; one loses 
the proposition in question, and wanders amidst a crowd of 
irrelevant details; another mistakes contraries for contradic- 
tories, or universal s for particulars; and, after some hours of 
storm, they know not what they have been discussing. One 
has made out a case which his adversary admits, the more 
readily as it has not the least bearing on the question ; 
another, having overthrown a similar collateral proposition, 
makes his pretended triumph resound over the field; yet 
another, having been rather shattered by reasons, appeals to 
the prejudices of his auditory, and, overwhelming his more 
rational antagonist with ridicule and abuse, comes off the 
apparent and acknowledged victor in the contest.'' * 

There are many subjects that have to be discussed at 
some length before it is possible to tell precisely what the 
point or points at issue are; but whenever there is a definite 
issue we should try very hard in our discussions and in our 
private thinking to stick to it. In our courts of law the rule 
that all testimony must be relevant is enforced very strictly. 
Unfortunately the corresponding rule about parliamentary 
discussions cannot be enforced so strictly. 

Two special forms of Ignoratio Elenchi are called the 
Argumentum ad Hominem and the Argumentum ad Popu- 
lum. These terms are applied in a rather loose includes 'ad 
sense to any argument that appeals to feeling or ^icminem'. 
that depends, not on the real question at issue, but upon 
the personality of any of the parties involved, including 
the hearers. As mere appeals to the desires or passions of 
one's hearers these arguments have been discussed already. 
As involving confusion between the real issue and some false 
issue they have not. As a form of Ignoratio Elenchi the 
Argumentum ad Hominem often consists in supposing that 
we have won our case because we have succeeded in em- 

* Davis, " Theory of Thought ", pp. 277-8. (Harpers, no date.) 



202 THE FORGOTTEN ISSUE. 

barrassing an opponent by some personal reference that 
has really nothing to do with it. If I am accused of ex- 
travagance I do not answer the accusation though I may 
silence the accuser by proving that he himself is no better; 
if my opinions are attacked I cannot substantiate them by 
replying that my opponent once held them himself. Such 
a retort I may have a perfect right to make, but I have no 
right to confuse it with a vindication of my own position. 

Undoubtedly it was the great danger of confusing issues 
when questions of personality are once introduced that made 
our common law exclude, as irrelevant all evidence as to the 
general character of the parties concerned even in cases in 
which such evidence might seem to the layman very relevant 
indeed. The courts try to decide each particular case on its 
individual merits, and not to give any man a favorable or 
unfavorable verdict merely because his general character is 
good or bad; they know that in many individual cases good 
men are in the wrong and bad men in the right; and they 
know enough about human nature to realize that if questions 
of general character are dwelt upon the jury will be 
influenced by them far more than they should be in order to 
decide the real question at issue on its merits. 

The Argujnentum ad Popidmn is practically indistinguish- 
able from the Argumeiiium ad Hominem. It is defined as 
*'an appeal to the passions, prejudices, etc., of the multi- 
tude ''. " The fallacy usually occurs in the course of long 
harangues, where the multitude of words and figures leaves 
room for confusion of thought and forgetful ness.'' . Here 
lies the danger of brilliant oratory and startling metaphors. 
Whatever one may believe to-day about the comparative 
values of a single and a double monetary standard of value, 
and the wisdom of suddenly changing from one to the 
other, it is certainly startling to think how half the country 
was swept away, in the spring of 1896, and a difficult 
economic problem for a time apparently settled, by a dazzling 
though empty metaphor about thrusting a crown of thorns 



INCLUDES 'AD HOMINEM'. 203 

upon the brow of labor and crucifying mankind upon a cross 
of gold. The real question at issue was, not whether labor- 
ing men should or should not be unjustly treated and man- 
kind in general oppressed, but whether a given policy would 
tend in the long run to diminish injustice and oppression, 
or to increase it. 



CHAPTER XX. 
THE ILL-CONCEIVED UNIVERSE. 

Logic deals, as we have seen, with the mutual implica- 
tions of relations. If the object A possesses the permanent 
quality B and the object C does not, we know 
assumed that A and C are not identical. Thus the pres- 

ence of a certain relation of subject and attribute 
in one case and its absence in another proves the absence of 
a certain relation of individual identity. These are the rela- 
tions concerned, but we can reason as we do about them 
only because we already know or assume that there are such 
things as separate individual objects, that these objects can 
have qualities, that qualities can be more or less permanent, 
that we are capable of recognizing the difference between 
qualities that are permanent and those that are not, and so 
on. These assumptions and probably a great many more 
form a sort of background for the reasoning in question. 
They constitute as it were the universe in which the relations 
specified in the syllogism exist, a universe without which 
they would lose entirely the significance which they now 
possess. It is a universe which human beings naturally take 
for granted; but if in the world to come we should discover 
that there are really no such things as separate individual 
objects and no such relations as those of subject and attri- 
bute, then we should be compelled to revise all our rules of 
logic and reason in some other way. A simple syllogism 
which seems to us now to be perfectly valid would then be 

204 



THE ASSUMED UNIVERSE. 205 

seen to be absolutely inconclusive. Indeed it would seem 
so inconsequent as to be utterly incomprehensible unless we 
co.uld remember our old earthly point of view — the universe 
in which we reasoned — and judge the argument from that 
standpoint. We could then say : ' Assuming the fundamental 
relations of things to be thus and thus, the reasoning is 
perfectly valid; but then these are no/ the actual relations; 
the blunder rested upon a wrong conception of the back- 
ground or universe, and it could not be corrected until that 
conception was outgrown '. 

In this example the relations which I have supposed to 
be improperly assumed are amongst the most fundamental 
relations of all reality. That is why the falsity of the 
assumption would involve the worthlessness of all our rules 
of formal logic. The universe of discourse included only 
relations common to the whole of the actual universe. Of 
course we human beings never in this life can test these most 
fundamental assumptions of all, and I suppose them to be 
questioned only for the sake of illustration. But as a matter 
of fact most of our reasoning is about matters in some 
special universe, where not only these but a great many 
other relations are taken for granted. That is why it is so 
difficult for any one but an expert in that particular field to 
criticise the logic in any scientific or other technical argu- 
ment. In even a game of whist, for example, it would not 
be possible to infer anything about your opponent's hand 
unless you knew the rules of the game, and even then the 
very perfection of your reasoning might lead you astray if 
you supposed he was playing the long game when as a matter 
of fact he was playing the short. So one might solve no 
end of chess problems with great ingenuity, yet get them all 
wrong, if he supposed that pawns always moved straight 
forward, that a queen could move like a knight, or that all 
the chessmen moved like checkers. 

A more serious example of the sort of thing I have in 
mind is found in Plato's '' Ph^edo ", Manv students who 



2o6 THE ILL-CONCEIVED UNIVERSE. 

read Socrates' argument for the immortality of the soul, there 
given, say that where the parties to the dialogue seemed to 
find the argument more or less conclusive, they can find no 
argument at all; or at least no connection between the 
premises and the alleged conclusions. The trouble is that 
they do not realize the conceptions of life which Socrates and 
his friends accepted as a matter of course. Throughout the 
dialogue it is assumed, for instance, that every living thing, 
whether animal or plant, must have a soul to give it life — to 
animate it. If to this is added the further assumption that 
new souls are not created, does it not follow that life would 
have ceased to exist ages ago unless the soul which animated 
one individual were reincarnated after the death of that indi- 
vidual in some other, and so in in scecula sceculorum ? Thus 
by getting back into Plato's universe — into the conceptions 
which serve as a background of the argument — we find sense 
where otherwise we find only nonsense; and if his argument 
seems to us inconclusive it is only because his universe 
seems unreal. 

Another instance of the same kind is found in the con- 
troversy between Locke and Leibnitz about innate ideas. 
Locke said it was absurd to suppose that the mind contained 
a set of ideas ready-made from birth, though we had no 
conscious knowledge of some of them until a great many 
years afterwards. Leibnitz replied that it was much more 
absurd to suppose that such ideas as those of right and wrong 
or of cause and effect could be conveyed into the mind 
through any one or all of the five senses. And so the dis- 
cussion proceeded, the adherents of each champion seeing 
the absurdities of the other. The conflict was necessarily 
interminable until in a later age it was realized that the 
advocates of both views assumed the same false universe, for 
everybody assumed that in some way or other the mind 
contains a kind of things called ideas which must have got 
there in some way or other. But it is really just as absurd 
to ask how the mind comes to contain its various ideas as 



THE ASSUMED UNIVERSE. 207 

to ask how a frog comes to contain its various jumps. A 
frog does not contain things called jumps; it merely acts in 
a way we call jumping; and the mind does not contain 
things called ideas; it thinks. 

So again with the deistic controversy about the possibility 
of miracles. Both sides took it for granted that the world 
had been wound up and started like a clock; but the deists 
said that God the clockmaker never intervened by a miracle 
to disturb its running, while the orthodox said he did. The 
question was one of intervention or non-intervention; and 
it did not occur to either side that nature was after all nothing 
but a visible and tangible aspect of God, not something sepa- 
rate with which perhaps he might not be able to interfere. 

And so it goes through the whole history of philosophy. 
Each age is dommated by some particular conception of the 
general constitution of things; and in that age the mutual 
relations of any particular facts are necessarily conceived w^ith 
reference to the assumed nature of the whole of which they 
are parts — of the background from which they stand out — 
of the frame into which they must fit. In the next age there 
is a new conception of the background — a new metaphor, 
perhaps, to express the deepest relations of things, — and the 
reasoning that before had seemed absolutely demonstrative 
now seems almost childish. 

In the cases just mentioned the assumption of the universe 
in question was xmconscious and practically inevitable. 
The same assumption of a universe is made consciously in 
the old Fallacy of Many Questions, e.g. : ' Have you cast 
your horns } ' ' Have you left off beating your father V 'Is 
the king of Eutopia dead } ' ' Why did you take my purse .? ' 
* Have you got over your fit of temper .? ' etc. Here of 
course the assumption is that you have had horns, that there 
is a king of Eutopia, etc., and it is impossible to answer 
either ' Yes ' or ' No ' to the question without seeming to 
admit the assumption.* 

* Sometimes the Fallacy of Many Questions is cornmitted to the em- 



2o8 THE ILL-CONCEIVED UNIVERSE. 

A Confusion of Universes occurs when we introduce into 
any universe something which cannot possibly be subject to 
the relations by which that universe is distin- 
confusionof guished, or when we introduce some other rela- 
tion which is inconsistent with them. All kinds 
of absurd questions rest upon such confusion. If you ask 
whether this triangle has eaten its dinner, I can hardly say 
even ' No ' without seeming to admit your absurd assumption 
that a triangle is the kind of thing that eats a dinner. Here 
of course there is an improperly assumed universe; but the 
assumption involves a more or less obvious incongruity. In 
his book on " The Nervous System and the Mind " * Charles 
Mercier points out with admirable clearness a somewhat 
less obvious incongruity of the same sort. 

*' It is not to be denied that there is a large amount of 
writing about the mind, and about the connection of the 
mind with the body, which is, strictly speaking, nonsense. 
. . . Such propositions are neither correct nor erroneous — 
neither true nor false. They are nonsense. . . . Take an 
instance. Try to think of a feeling passing along a nerve. 
We often speak familiarly of a toothache shooting along a 
nerve; is this an accurate expression } Take the nerve. 
Dissect it out. Lay it on the table before you. It is a gray 
thread, four inches long, made up of fibres bound together. 
Now take a toothache and set it running along the nerve. 
You cannot. Why } It ran along the nerve, you said, 
when it was m the body; why cannot it do so now .? 
Because, you will say, the nerve is no longer connected with 

barrassment of the questioner instead of the person questioned. Many of 
the typical Irish jokes belong to this class, such for example as the story 
of the Irishman who was being tried for assaulting a Chinaman in front 
of the Palmer House and had arranged with a friend to prove an alibi. 
He conducted his own defence and when the time came to question the 
witness he put in some preliminary flourishes and continued : ' Then, 
Patrick Murphy, on your oath, sir, where was I when I struck the 
Chinaman in front of the Palmer House ? ' 
^ Macmillan, i88S. 



THE CONFUSION OF UNIVERSES. 209 

the brain. Take another nerve, then, and do not separate 
it from the body; but pinch it, cut it, burn it, or galvanize 
it. What torture! what excruciating agony! Surely this 
pain is in the nerve; you feel it there. Wait a little; let us 
consider. The nerve is made up of axis-cylinders and 
padding; in which is the pain ? Certainly not m the 
padding; it must then be in the axis-cylinders. The axis- 
cylinders are gray threads of protein substance, which is 
made up, like all other matter, of molecules swinging m 
space. Now, where is the pain ? Is it m the molecules or 
m the intervening space ? And how does it pass along the 
nerve ? Does it jump from molecule to molecule, or does 
it flow in the interstices ? If the former, pain must be a 
solid; if the latter, it must be a fluid; both of which 
hypotheses are manifestly nonsense. There is a third alter- 
native. It may be a movement communicated from molecule 
to molecule. . . . Consider again. Imagine the molecules 
of the nerve swinging in space. Now imagine a wider swing. 
Does that resemble pain } Turn the circle into a spiral. Is 
that like pain } But it may be said. Pain, we know, is not 
really m the nerves, it is in the brain. Again the same 
problem awaits us. The brain is made of cells and fibres. 
Is pain in the cells } Is it in the fibres } In either case we 
must come down to molecules at last, and again the pain 
eludes our search. No conceivable form of matter and no 
conceivable movement of matter bears the smallest resem- 
blance to pain, or can by any human imagination be assimi- 
lated to pain. We are driven to the conclusion that pain 
and matter are things with no community of nature, are 
facts of totally different orders, and cannot be reduced to 
any common term. Pam is neither in the nerves, nor in the 
brain, nor in any position in space. It is in the mind." 
And of course this expression ' in the mmd ' simply means 
that we feel it. 

Fallacies of False Analogy may often be regarded as cases 
of an ill-conceived^ and perhaps of a confused, universe, 



2IO THE ILL-CONCEIVED UNIVERSE. 

r 

The bare facts or some of them may be known accurately 
enough, but the relations between them — the general back- 
ground in which they are set — is conceived erroneously. 
'* Carlyle's saying that a ship could never be taken round 
Cape Horn if the crew were consulted every time the captain 
proposed to alter the course, if taken seriously as an analog- 
ical argument against Representative Government, is open 
to the objection that the differences between a ship and a 
State are too great for any argument from the one to the 
other to be of value. It was such fallacious analogies as 
these that Heine had in view in his humorous prayer, 
* Heaven defend us from the Evil One and from meta- 
phors \^'* 

Often as we turn from one aspect of a situation to another 
we find some new fact which is not consistent with some 
general statement that we made about the first aspect; and 
this may lead to a ' hulV , 'One man is as good as 
another ', says the Irishman when he resents the claim of 
superiority made by some one else; but as he thinks of his 
own excellences and the other's shortcomings he adds, ' and 
sometimes a long sight better'. Sometimes the bull is due 
to an unfortunate metaphor; e.g,, ' Our cup of sorrow is 
overflowing, and is not yet fall \ 

Since every metaphor rests on the assumption, though even 
for only a moment, of a kind of universe, every case of mixed 
metaphors is a case of confused universes. I take the follow- 
ing from Genung's '* Rhetoric '' : '' The very recognition of 
these or any of them by the jurisprudence of a nation is a 
mortal wound to the very keystone upon which the whole arch 
of morality reposes.'' — " This world with all its trials is the 
furnace through which the soul must pass and be developed 
before it is ripe for the next world." — " I write to you in a 
state of mind that I really ardly know what I am about, but 
I cannot indure making no effort to clear up the gaping abiss 

* Minto's ''Logic", p. 373. 



THE NEGLECTED ASPECT. 211 

which the events of the past fatal afternoon has raised between 
us." 

Another kind of ill-conceived universe may be called the 
Universe with a Neglected Aspect. This phrase is intended 
to include all arguments in which the existence or influence 
of some essential relation or object in the uni- Theneg- 
verse involved is neglected. In calculating the l^^ted aspect. 
time it will take a feather dropped from the window to 
reach the ground we have a right to neglect the attraction 
exerted upon the feather by some fixed star, for though 
there is such an attraction it makes no appreciable differ- 
ence in the result, and we have a right to neglect the death 
of some Asiatic despot, for it makes no difference at all in 
the result — is not in the universe under consideration. But 
we have no right to neglect the resistance of the air, or the 
influence of the wind with all its gusts and eddies; for they 
make every possible difference in the result. Similarly we 
have no right to conclude that free trade is necessarily the 
best policy for some particular state, merely because it is 
always or usually the policy most favorable for the accumu- 
lation of wealth, unless we have first made sure that there 
is no question of education, or public morals, or military 
necessity, or international politics, which demands some 
other policy. 

Every roseate picture of the happiness to be attained when 
the competition of commercial rivals has ceased, and the 
State controls all industry and gives every one his due, is 
painted in happy forgetfulness of the natural discontent, 
selfishness, laziness, or ambition which would prompt most 
of the people in such a community to shirk their appointed 
tasks, to use personal influence in order to get some special 
privilege, or to gain control of the machinery of government 
for the particular benefit of themselves and their friends, — 
forces in human nature which would replace commercial 
competition with political jobbery. 

Under the head of Composiiion, Whately gives several 



^i^ The ILL-CONCEIVED UNIVERSE. 

examples of what I should rather call a neglected relation of 
articulation : 

" There is no fallacy more common or more likely to 
deceive than the one before us: the form in which it is most 
usually employed is to establish some truth, separately, 
concerning each single member of a certain class, and then 
to infer the same of the whole collectively; thus some infidels 
have labored to prove concerning so7ne one of our Lord's 
miracles, that it might have been the result of the accidental 
conjuncture of natural circumstances; next they endeavor 
to prove the same concerning another, and so on; and 
thence infer that all of them might have been so. They 
might argue in like manner, that because it is not very im- 
probable that one may throw sixes in any one out of a 
hundred throws, therefore it is no more improbable that one 
may throw sixes a hundred times running." 

This is, as we have said, a case of neglected articulation. 
The miracles in question all took place within a certain short 
period and were all connected with a single personality. 
The general fact that one supposed miracle is shown to be 
the result of accident would be a reason for, and not against, 
the belief that a great many others could be explained in the 
same way; but if these others are accidents and not really 
miracles we should expect to find them scattered, not 
grouped and articulated as they are in the case in question. 
So with the throws of sixes. It is not the occurrence of a 
hundred of them that is remarkable, but of a hundred in 
succession with the same dice and m the hands of the same 
player.* 

* This argument of Whately's is perfectly valid as a reply to those 
who try to explain the miracles in question by a series of physical acci- 
dents. But if it be taken as an independent proof of their miraculous 
nature it might be itself regarded as an example of the Neglected Aspect; 
for it fails to consider the mental influences which tend to produce this 
very grouping. It is easier to hypnotize one person if others have been 
hypnotized in his presence, and for much the same reason the ' cures * 
wrought by our modern faith doctors generally come in groups. 



Tim NEGLECTED ASPECT. 21;J 

Often the neglected relation is one that is necessarily and 
obviously involved in some general scheme that is contem- 
plated, and the neglect to consider it must be charged, not 
to ignorance, but to sheer haste and carelessness. " From 
the circumstance that some men of humble station, who 
have been well educated, are apt to think themselves above 
low drudgery, it is argued that universal education of the 
lower orders would beget general idleness; this argument 
rests, of course, on the assumption of parallelism in the two 
cases, viz., the past and the future; whereas there is a cir- 
cumstance that is absolutely essential, in which they differ; 
for when education is universal it must cease to be a distinc- 
tion; which IS probably the very circumstance that renders 
men too proud for their work. " ^ 

This blunder is like that of the people who clamor for 
some change in the tariff or in the currency that will give 
everybody ' more money ', forgetting that if dollars were as 
common as pebbles they would be worth no more than 
pebbles, and all that one could carry would hardly buy a 
dinner; or like that committed by the member of a crowded 
audience who asked that everybody present might be allowed 
to stand on the back of his seat and thus get an unobstructed 
view of the performance. 

The blunder of a Neglected Aspect is involved in every 
philosophical theory which resolves all reality into mere 
phenomena, forgetting that there can be no phenomenon or 
appearance without something to appear and some one to 
whom it appears. It is involved in the old myth of Atlas 
supporting the world; for any object that requires to be 
supported does so because it is heavy, i,e., because it is 
attracted by every other object and therefore tends to move 
towards the common centre of gravity. But as there is 
nothing outside of the world (or at least outside of the uni- 
verse) towards which it is attracted, the universe as a whole 

* Whately, op. cit. 



2 14 THE ILL-CONCEIVED UNIVERSE. 

does not tend to fall, or in other words, it has no weight at 
all. Another such absurdity is involved in the question 
' Where is the universe ? ' To tell the position of any par- 
ticular object is to tell how it lies with reference to some 
other object or objects; but the universe contains all objects 
• — it would not be the universe if it did not — and therefore 
there is nothing lying outside of it by which it can be 
located : it has no place. What has been said about the place 
of the world is applicable, mutatis mutandis, to questions 
about its cause and the time at which it came into existence. 
A similar criticism can be applied to the question * Is life 
worth living .? ' To ask what a thing is worth is to ask what 
people are willing to take in exchange for it — what other 
object they believe will give them as much satisfaction. But 
all exchange, all weighing of alternatives, all satisfaction and 
dissatisfaction presuppose a life in which they take place, 
and to ask what this life itself is worth is as absurd as to try 
to weigh your balances in their own pan. 

In all such cases the universe as a whole — the total system 
of related objects — is spoken of as though it could possess 
relations which exist only between various members within 
it. 

Dilemmas of the epigrammatic sort are almost always based 
upon a view of only half the universe, and for this reason 
*' can often be retorted by producing as cogent a dilemma to 
the contrary effect. Thus an Athenian mother, according 
to Aristotle, addressed her son in the following words : * Do 
not enter into public business; for if you say what is just, 
men will hate you; and if you say what is unjust, the gods 
will hate you '. To which Aristotle suggests the following 
retort: ' I ought to enter into public affairs; for if I say what 
is just, the gods will love me; and if I say what is unjust, 
men will love me. ' '' (Jevons.) Again, Epictetus says that 
if honors which we do not possess are good, we should rejoice 
that another has them ; if bad, that we have them not. But 
a pessimist might reply that if they are good, we should grieve 



THE NEGLECIED MEMBER. 215 

that we have them not; if bad, that another has them. 
What EpictetLis says, therefore, amounts merely to this: that 
we should look on the bright side of things and deliberately 
ignore the other side. This certainly is a healthy practical 
attitude, but when one begins to theorize he must see both 
sides. 

Often, as Lotze points out,''' an aspect of a situation, 
though mentioned, can be crowded out of view by the mere 
order of a sentence. To say ' I am a great deal better off 
than he is ' is more cheerful than to say ' He is worse off 
than 1 am ' ; but the facts of the case are the same. This is 
so also with the saying ' There is a silver lining to every 
cloud ' and its converse, ' There is a cloud to many a silver 
lining '. " Think of public teachers who say that the farmer 
is ruined by the cost of transportation, when they mean that 
he cannot make any profits because his farm is too far from 
the market. " f 

When the whole background is not misconceived or dis- 
torted or a part of it overlooked, we may still err by over- 
looking some member of the universe, coordinate 

The 
with those under discussion, whose influence ne§:lected 

(or at least whose presence) ought to have been 
taken into account. If A, B, C, and D are fixed points on 
a given plane, I may be able to determine the relations of any 
one of them to any other without any reference to the rest ; but 
if they are planets, each attracting every other, I cannot do 
this. If any member of the system is ignored, any prediction 
I may make with reference to the others is bound to turn 
out more or less erroneous. It is here that we find the fallacy 

* '' It maybe said that evil appears only in particulars, and that when 
we take a comprehensive view of the great whole it disappears; but of 
what use is a consolation the power of which depends upon the arrange- 
ment of clauses in a sentence ? For what becomes of our consolation if 
we convert the sentence which contains it thus — The world is indeed 
harmonious as a whole, but if we look nearer it is full of misery ? ** Mi- 
crocosmus, Bk. IX, Ch. V (Scribners). 

I Sumner, op. cit., p. 46. 



2i6 THE ILL-CONCEIVED UNIVERSE. 

of the old argument in favor of a protective tariff, ' Gold and 
silver are wealth; a protective tariff, by shutting out imports 
while not interfering with exports, increases the gold and 
silver in a country; it therefore increases the country's 
wealth. ' Assuming the truth of the premises, the conclusion 
does not follow, because while gold and silver are wealth 
they are not the only forms of wealth, and the imported gold 
and silver must be paid for by some other kind of wealth 
exported. The fallacy lies in forgettmg this exported 
wealth — in looking at only a part of the universe or system 
in question. 

So, many an unfortunate maintains that he * has a right to 
a living \ or to certain comforts; forgetting that such a right 
on his part implies a duty to provide him with these things 
on the part of somebody else. 

The best account that I know of this fallacy of the for- 
gotten member of the universe is to be found in the little 
book by Professor Sumner already quoted. 

''the forgotten man/' 

'' In all jobbery the case is the same. There is a victim 
somewhere who is paying for it all. The doors of waste and 
extravagance stand open, and there seems to be a general 
agreement to squander and spend. It all belongs to some- 
body. There is somebody who had to contribute it, and 
who will have to find more. Nothing is ever said about 
him. Attention is all absorbed by the clamorous interests, 
the importunate petitioners, the plausible schemers, the 
pitiless bores. Now, who is the victim ? He is the For- 
gotten Man. If we go to find him, we shall find him hard 
at work tilling the soil to get out of it the fund for all the 
jobbery, the object of all the plunder, the cost of all the 
economic quackery, and the pay of all the politicians and 
statesmen who have sacrificed his interests to his enemies. 
We shall find him an honest, sober, industrious citizen, 
unknown outside his little circle, paying his debts and his 



THE NEGLECTED MEMBER. 217 

taxes, supporting the church and the school, reading his 
party newspaper, and cheering for his pet politician. 

" We must not overlook the fact that the Forgotten Man 
is not infrequently a woman. I have before me a newspaper 
which contains five letters from corset-stitchers who complain 
that they cannot earn more than seventy-five cents a day 
with a machine, and that they have to provide the thread. 
The tax on the grade of thread used by them is prohibitory 
as to all importation, and it is the corset-stitchers who have 
to pay day by day out of their time and labor the total 
enhancement of price due to the tax. Women who earn 
their own living probably earn on an average seventy-five 
cents per day of ten hours. Twenty-four minutes' work 
ought to buy a spool of thread at the retail price, if the 
American workwoman were allowed to exchange her labor 
for thread on the best terms that the art and commerce of 
to-day would allow; but after she has done twenty-four 
minutes' work for the thread she is forced by the laws of her 
country to go back and work sixteen minutes longer to pay 
the tax — that is to support the thread-mill. The thread- 
mill, therefore, is not an institution for getti .g thread for the 
American people, but for making thread harder to get than 
it would be if there were no such instituti^- n. . . . It makes 
a great impression on the imagination, nowever, to go to a 
manufacturing town and see great mills and a crowd of 
operatives; and such a sight is put forward, under the special 
allegation that it would not exist hut for the protective tax, as a 
proof that protective taxes are wise. But if it be true that 
the thread-mill would not exist but for the tax, then how 
can we form a judgment as to whether the protective 
system is wise or not unless we call to mind all the seam- 
stresses, washerwomen, servants, factory-hands, saleswomen, 
teachers, and laborers' wives and daughters, scattered in the 
garrets and tenements of great cities and in cottages all over 
the country, who are paying the tax which keeps the mill 
going and pays the extra wages } If the sewingwomen, 



2l8 THE ILL-CONCEIVED UNIVERSE. 

teachers, and washerwomen could once be collected over 
against the thread-mill, then some inferences could be drawn 
which would be worth something. Then some light might 
be thrown upon the obstinate fallacy of ' creating an indus- 
try ', and we might begin to understand the difference 
between wanting thread and wanting a thread-mill. Some 
nations spend capital on great palaces, others on standing 
armies, others on iron-clad ships of war. Those things are 
all glorious, and strike the imagination with great force when 
they are seen; but no one doubts that they make life harder 
for the scattered insignificant peasants and laborers who have 
to pay for them all. They ' support a great many people ', 
they ' make work ', they ' give employment to other indus- 
tries '. We Americans have no palaces, armies, or iron-clads, 
but we spend our earnings on protected industries. A big 
protected factory, if it really needs the protection for its 
support, is a heavier load for the Forgotten Men and Women 
than an iron-clad ship of war in time of peace. 

"It is plain that the Forgotten Man and the Forgotten 
Woman are the real productive strength of the country. 
The Forgotten Man works and votes — generally he prays — 
but his chief business m life is to pay. His name never gets 
into the newspapers except when he marries or dies. He is 
an obscure man. He may grumble sometimes to his wife, 
but he does not frequent the grocery, and he does not talk 
politics at the tavern. So he is forgotten. Yet who is there 
whom the statesman, economist, and social philosopher 
ought to think of before this man ? If any student of social 
science comes to appreciate the case of the Forgotten Man, 
he will become an unflinching advocate of strict scientific 
thinking in sociology, and a hard-hearted sceptic as regards 
any scheme of social amelioration. He will always want to 
know, Who and where is the Forgotten Man in this case, 
and who will have to pay for it all .? " ^ 

* Sumner, op. cit., pp. 145-149. 

Since the forgotten member is always a member related to the rest of 



THE NEGLECTED WHOLE. 219 

The examples so far given have all shown a universe 
unduly curtailed or simplified through the neglect to con- 
sider some one or more of its essential relations 

The 
or members. But there are cases in which the neglected 

. . . , , whole, 

very existence of a universe of interrelated mem- 
bers seems to be ignored. To quote Whately once more 
(though here again he gave the example under another 
head) : 

"When a multitude of particulars are presented to the 
mind, many are too weak or too indolent to take a compre- 
hensive view of them; but confine their attention to each 
single point, by turns: and thus decide, infer, and act 
accordingly : e.g., the imprudent spendthrift, finding that 
he is able to afford this, or that, or the other expense, forgets 
that all of them together will ruin him. 

'' To the same head may be reduced that fallacious 
reasoning by which men vindicate themselves to their own 
conscience and to others, for the neglect of those undefined 
duties, which though indispensable, and therefore not left to 
our choice whether v/e will practise them or not, are left to 
our discretion as to the mode, and the particular occasions, 
of practising them; e.g., ' I am not bound to contribute to 
this charity in particular; nor to that; nor to the other': 
the practical conclusion which they draw is, that all charity 
may be dispensed with.'' 

In each of these cases the trouble lies, as Whately so 
clearly says, in the failure to " take a comprehensive view " 
of the universe as a whole. In the former case we forget 
that when a given variable (namely, the money at one's 
disposal) is placed there it cannot also be placed here; in 
the latter we forget that if the variable (namely, charity) is 
not placed there, it ought to be placed here, since it ought 
to have a place somewhere or other in the universe. 

The same failure to keep the whole universe and its rela- 

the system, no hard and fast line can be drawn between a case of the 
forgotten member and a case of the forgotten relation. 



2 20 THE ILL-CONCEIVED UNIVERSE. 

tions in view accounts for what Whately calls the Fallacy of 
Objections, i.e., " showing that there are objections against 
some plan, theory, or system, and thence inferring that it 
should be rejected; when that w^hich ought to have been 
proved is, tliat there are more, or stronger, objections against 
the receiving than the rejecting of it. . . . For there never 
was, nor will be, any plan executed or proposed, against 
which strong and even unanswerable objections may not be 
urged; so that unless the opposite objections be set in the 
balance on the other side, we can never advance a step.'' 

This Fallacy of Objections is peculiarly characteristic of 
people whose energy is small but whose moral or aesthetic 
sensibilities are morbidly developed. They should help to 
pay a detective to catch a thief, and refuse because a detec- 
tive's work is not straightforward and frank; they should 
help to hang a murderer, or should shoot a murdering 
burglar to secure the safety of honest people, and hold back 
because it is cruel; they want the liquor traffic cut down 
and they are convinced that a license system is the only thing 
that will do it, but they object to this because it makes the 
government ' a partner in sin ' ; they should wash their 
clothes, but they are afraid of soiling their fingers. Perhaps 
there is some relation in life in which each of us strains for 
ever at gnats and swallows camels. We see the gap in the 
universe, but there is no ideal material at hand, so we let it 
go unfilled: 

** Our common problem, yours, mine, every one's, 
Is, not to fancy what were fair in life 
Provided it could be, but finding first 
What can be, then find how to make it fair 
Up to our means ; a very different thing." 



CHAPTER XXL 
THE DIFFERENCE BETWEEN INDUCTION AND DEDUCTION. 

The student who has followed the preceding chapters at 
all thoughtfully has doubtless been impressed by a keen and 
disappointing sense of limitation : there are so many things 
that we must not do, and so few that we may, so 

many cautions to hold us back, and so few posi- in 

. . 1 . 1 1 rj^-i- . . limitations, 

tive principles to help us on. Ihis impression 

is well founded. The principles of deductive logic are im- 
portant indeed and should never be forgotten : and yet if any 
one dwells on them exclusively, and forgets that cautions 
would be worthless in the absence of some positive forward 
impulse, he is likely to become a mere carping critic ; a fault- 
finder, who is forever detecting flaws in the reasoning of 
others, but utterly incapable of doing any constructive work 
of his own. 

Induction is that part of logic which is concerned with the 
onward movement that deduction cannot undertake. Its 
essential task can be best understood by looking once more 
at the limitations of the syllogism and then seeing how it 
tries to supplement them. The first figure teaches that if 
every A is a B and every B is a C, it is safe to conclude that 
every A is a C. But it does not tell how to find out in the 
first place that every A is a B or that every B is a C. It 
proceeds in this case, as they say, from generals to particu- 
lars, but not from particulars to generals. Induction tells us 
how to prove in the first place that every A is a B or that 

?2I 



22 2 INDUCTION AND DEDUCTION. 

every B is a C ; how to get from particulars to generals. 
The second figure teaches that dissimilarity proves objects 
not to be identical ; but it does not help us to prove that ob- 
jects are identical. Induction does. The third figure teaches 
that the coexistence of relations proves that they are com- 
patible, that they 77iay come together ; but it does not try 
to prove that they are necessarily connected, so that they ;;^^j^/ 
come, together. Induction does. Thus in the case of each 
figure induction attempts a task in the presence of which de- 
duction is helpless. This work of getting more general or 
more positive or more emphatic results than those reached by 
the syllogism is not the whole of inductive logic any more 
than the syllogism itself is the whole of deductive ; but, like 
the syllogism in deduction, it is the heart of the subject.* 

AVhy Induction is able to go ahead and do more than De- 
duction we shall understand better when we have reached the 
close of the next chapter, and better still when we have gone 
farther. But there are three things about Induction by which 
we can explain at least a part of the difference now. 

In the first place, every system of Induction rests on the 
assumption that facts of true logical significance can be attained 
by direct observation. If a person whose mental life was 
limited to deductive reasoning were asked whether the man 
in front of him had light hair or dark, he might be in posses- 
sion of some premises that would enable him to answer the 
question or he might not ; and if he had no such premises, he 

* It is often said that the difference between Deduction and Induction 
is that the one proceeds from generals to particulars, while the other pro- 
ceeds from particulars to generals; that is to say, that deducticm pro- 
ceeds from statements about classes of things to statements alxjut smaller 
classes or about individuals, while induction proceeds Irom statements 
about individuals to statements about classes. But in deduction it is only 
the first figure of the syllogism that goes from statements about classes to 
statements about the individuals in them; and in induction it is only the 
process corresponding to the first figure that is concerned with mere 
generalization. This statement, therefore, is based upon too narrow a 
view of the scope of both branches of Logic, 



DIFFERENCE IN LIMITATIONS. 223 

could not answer it. But the one thing which he could not 
do would be to look at the man and see. Reasoning abso- 
lutely limited to deduction is eminently suited to people like 
the monastic scholars of the middle ages who did not profess 
to possess any other source of true knowledge than the writ- 
ten word of the Church as found in some recognized author- 
ity, such as the Bible or the works of Aristotle or St. Thomas. 
To the orthodox Scholastic every o[)inion at variance with 
such authorities was not only false but wicked. " There is a 
characteristic anecdote of Scheiner, who contests with Galileo 
the honor of being the first to observe the spots in the sun. 
Scheiner was a monk; and, on communicating to the superior 
of his order the account of the spots, he received in reply 
from that learned father a solemn admonition against such 
heretical notions: VI have searched through Aristotle,' he 
said, ' and can find nothing of the kind mentioned ; be 
assured, therefore, that it is a deception of your senses or of 
your glasses.' " * Thus, to the Scholastic, the data for reason- 
ing were all given by some authority, and usually in the form 
of general propositions. In contrast with this, Induction 
supposes us to be set loose in the world with all our senses 
about us to collect our own data; to find the straw as well 
as to make the bricks. 

Now all observation is of individual facts. General truths 
may be inferred ; but the facts on which they are (or should 
be) based must be observed one at a time. Consequently, 
while the Deductive reasoner is accustomed to appeal for the 
most part to general principles of some sort by way of prem- 
ises, and thus learns to regard such principles wath a cer- 
tain veneration, the Inductive reasoner is appealing all the 
time to individual facts as revealed by the senses, and he 
gives a large share of his veneration to them. Hence the 
saying that in science a single fact is worth a bushel of theory. 

In the second place. Induction distinctly recognizes the 

•^ Baden Powell's '' History of Natural Philosophy", p. 171. Quoted 
in Fowler's ''Inductive Logic", p. 293. 



2 24 INDUCTION AND DEDUCTION. 

presence of change in the world. It may be remembered that 
the relations of things (as distinguished from the laws oi 
thought pure and simple) upon which deductive reasoning 
turns are individual identity, similarity, and the coexistence 
of qualities or other attributes. Now all three of these rela- 
tions could exist — identity after a fashion and the other two 
very well — in a world in which there was no change, in which 
nothing ever happened or came to pass ; and it may be re- 
membered that this notion of change was so remote from the 
conception of the universe involved in deduction that the 
rules of the syllogism have been declaring for centuries that 
contrary relations prove objects to be non-identical, without 
ever stopping to say that this rule only holds when the objects 
in question are observed at the same time, or at least nearly 
enough at the same time to make it certain that these par- 
ticular relations could not have changed. Induction on 
the other hand has to do almost altogether with a world of 
change; and for it the most important relation of all is the 
relation of one change or event to another. 

A third characteristic of induction is that it rests at bottom 
upon a tendency, unconscious or conscious, vague or definite, 
to act as though we took for granted that in the changes 
and other relations of things we might expect a certain uni- 
formity. This tendency is so important that we must pre- 
sently give a longer account of it. 

The fourth characteristic of Induction is that when it reaches 
the critical stage it attempts more or less seriously to find out 
and examine every case of a given sort in the world or the 
part of the world under consideration. Let us explain this 
with reference to each of the figures separately. 

If we wish to find out whether it is true that every mem- 
ber of a certain family has light hair, the simplest inductive 
method is to look at each one of them, and if we find none 
that have not and if we are sure that we have examined them 
all, we can be sure that the statement is true. In this way 
we are able to gain the singular or the universal proposition 



DIFFERENCE IN LIMITATIONS. 225 

which is required as one of the premises of a deductive argu- 
ment in the first figure. 

According to the second figure dissimilarity proves that 
objects are not identical, but similarity does not prove that 
they are. What then will prove it? If I leave a book of 
mine in a library and the next day find one there which 
looks precisely like it, how can I make sure that it is mine, 
and not some other copy of the same work ? I can make 
sure of it if I make sure that no book has gone out of the 
library since mine was left there, and then examine every 
book in it, but find no other that looks precisely like the one 
that I left. Similarity will not ordinarily prove identity, for 
there is no limit to the number of things that may resemble 
each other ; but if we are certain that some former object 
still exists in a certain part of the world and still retains its 
former appearance, and if we are equally certain that in that 
part of the world there is now only one object with that ap- 
pearance, we may be certain that the two are identical. Thus 
by a sufficiently exhaustive examination of other things we 
can prove the identity of those in question, where the second 
figure of the syllogism which does not look beyond the objects 
given can prove only non-identity. 

The third figure proves from the coincidence of two given 
relations that they are compatible ; but it can never go further 
and prove, that they are necessarily connected. Induction 
can ; and again it proceeds by going beyond the two given 
relations and attempting to consider a worldful. Suppose 
for example that an event A is immediately followed by the 
event K. For deduction this proves that the succession of 
these two events, A and K, is not impossible ; and for induc- 
tion this one case taken by itself proves nothing more. But 
if we assume, as induction does, that every event has a 
cause with which it is necessarily connected, and if there is 
any way — whether direct or indirect — of going over all the 
events which preceded K and of showing that there was no 
event but A which could have caused it, then we can be 



2 26 INDUCTION AND DEDUCTION. 

quite sure that A did cause it. And something of this sort is 
what induction attempts. 

Thus there is an inductive process corresponding to each 
figure of the syllogism, and in each case the inductive process 
attempts to reach conclusions which the deductive does not, 
by looking beyond a mere pair of given relations and at- 
tempting to exhaust the universe. 

One of the most obvious differences between deduction 
and induction is that in deduction any conclusion that fol- 
lows from the given premises at all seems to fol- 
Difference , .1,1 • ,.,.-.,. 

in low With absolute certainty, while m inductive 

certainty. i r n -.i 1 

reasoning it only follows with a greater or less 

degree of probability. This difference is striking and im- 
portant, and it is sometimes thought to depend upon some 
absolutely fundamental difference between the two methods. 
But it does not. So far as the strictly demonstrative side of 
the two is concerned their problems are precisely the same, 
namely : to" find whether the conditions named in the pre- 
mises could exist in the assumed universe in the absence of 
t?ie conditions named in the conclusion. The difference in 
certainty is due merely to the greater complexity of the ma- 
terial which induction attempts to handle. In the first place, 
the relations of things — the laws of the universe — which in- 
duction has to assume are more complex ; in induction we 
must reckon with the uniformity of nature and ail that that 
implies as well as with the simpler relations of things assumed 
in deduction. Then, in the second place, the particular 
facts that have to be built together according to the general 
relations of our universe are — as we have seen — ever so much 
more numerous in induction — often indeed innumerable, and 
even when we know that all the facts are in our possession 
it is a much more difficult and uncertain thing to realize how 
they must all fit together when there are a great number of 
them than when there are only tw^o. Moreover, in induc- 
tion, where the ideal is to search through the whole world 
and find every fact of a given sort, we usually know perfectly 



DIFFERENCE IN CERTAINTY. 227 

well that the search has been incomplete, and even when we 
have tried to make it complete there is always the chance 
that something has been overlooked and that we really have 
not exhausted the universe after all. This is why the induc- 
tive sciences are being continually corrected, while such a 
science as geometry (which does not demand this exhaustive 
search through the world) stands from the first with little or 
no correction. Assume the uniformity of nature, and a 
* perfect induction ', or one which really exhausted the uni- 
verse in question, would give quite as much certainty as de- 
duction ; but in this complex world of which we are so 
ignorant, perfect induction is little more than an ideal. We 
come as near to it as we conveniently can and then begin to 
guess, trusting to future experience to correct us if the guess 
is wrong. But the fact that in induction we often have to 
guess for lack of premises or for lack of skill to put them 
together does not prove that if anybody had the premises and 
had the skill his inductive construction of facts would be 
any less infallible than his deductive. 



CHAPTER XXII. 

THE UNIFORMITY OF NATURE. 

According to the old definition, '^ Man is a rational ani- 
mal ' ' ; and to say this means much more than merely to say 
he is rational. Animals are distinguished from sticks and 

How we stones by the fact that they can feel and move, 

come to ^, . 1 r . . 

believe in it. The movement comes m response to the feeling; 

but animals differ from each other with respect to the con- 
nection between the two. With some the movement follows 
upon the feeling directly, uniformly, and, so far as we can 
judge, inevitably. Others can postpone the movement until 
they have stopped and considered. Man can stop longer 
and consider more than any other animal, and for that reason 
he is called pre-eminently rational. But even man cannot 
always stop and consider how to act in response to his im- 
pressions. He cannot help swallowing anything which has 
begun to go down his throat ; he cannot endure more than a 
certain amount of pain without crying out ; and without con- 
siderable training he cannot avoid raising his arms, shutting 
his eyes, or drawing his head back when a blow is aimed at his 
face. Reflex acts like these shade so imperceptibly into the 
acts which we call purely voluntary that it is often impossi- 
ble to say whether some act, even if it is our own, belongs to 
the one class or to the other. Moreover, there is good rea- 
son to believe that all voluntary acts are built up on a basis 

228 



HOW WE COME TO BELIEVE IN IT. 229 

of those which are purely reflex and instinctive ; so that if we 
did not resemble the lower animals in performing the latter 
we should never be capable of the former ; and if this were 
the case — if we could not perform a voluntary act — there 
would be no use in considering what act would be best. 
This means there would be no use in reasoning ; for sooner 
or later all reasoning in this world has reference to some 
possible act. Therefore, as man is actually constituted, his 
being rational is connected in the closest possible way with 
being an animal, subject to all sorts of impressions from the 
world outside, and bound to respond sooner or later to these 
impressions by some kind of action. 

The advantage which man possesses of being able to stop 
and consider how to act longer than any of the other animals 
is not without its dangers. To let an opportunity for action 
go by is often quite as fatal as to act rather stupidly. A fox 
that considered too long because he feared a trap would soon 
starve to death, and a man who never did anything until it 
was too late would get along as badly as one who acted on 
every impulse as soon as it arose. What we need is some 
way of combining the advantages of both kinds of action, 
the wisdom of the deliberate with the rapidity of the purely 
reflex or impulsive ; and this we get in a large measure 
through our capacity for forming habits. When an act has 
been advantageous we tend to do it again under similar cir- 
cumstances, and every time we repeat it it becomes more 
spontaneous, easy and rapid, until at last it becomes to all 
intents and purposes purely instinctive or reflex. These 
results of habit are very useful in the main. Of course habit 
has its drawbacks as well as its advantages; for occasionally 
we form habits that are bad from the beginning, and some- 
times an exceptional condition of things will make a mode 
of action which is generally good extremely inappropriate. 
But the race would not have acquired and kept the habit- 
forming tendency at all except in adjustment to a world in 
which there is uniformity enough to make it profitable. 



230 THE UNIFORMITY OF- NATURE. 

Mental anticipations are one form of habit. These do 
not seem to come at first in the form of anything so definite 
as a judgment. The new-born child does not say ' Now I 
shall see this or feel that '. He does not ask ' Is it to 
be so or is it not ? ' and then answer his own question 
in the affirmative. There is no antithesis between ' Yes ' 
and ' No '. There is only a purely reflex expectation. The 
image of the anticipated experience enters the mind and 
fills it. But the anticipation comes nevertheless, and thus 
in the imagination, as in the muscles, the nervous system 
produces a very naive and elementary form of expectation. 
This expectation when it arises is not, as some philosophers 
used to think, derived from any ' innate principle ' or ' im- 
plicit ' or ' unconscious ' thought that nature is always 
uniform; but in each particular case the particular expecta- 
tion arises spontaneously and mechanically as a result of 
habit. 

All this is only to say that man is a creature of habit 
because he has to live in a world in which Nature is uniform. 
It does not tell how we came to believe in that uniformity. 
The blind tendency to form habits and thus act as though 
order were to be expected in the world is something very 
different from the explicit thought that it exists; and yet 
without the former it is difficult to see how we could have 
gained the latter. The process by which the one leads to 
the other is something like the following. 

As the child gets along in life and his expectations are 
sometimes disappointed he gains a sense of the difference 
between the images and expectations that arise from within 
and the experiences that come from without, i.e., between 
thoughts and realities; and at the same time he gains a sense 
of the difference between the thoughts that correspond to the 
realities and those that do not; i.e., between the true which 
he can welcome with the judgment ' Yes, it is so ' and the 
false that he must reject with the judgment ' No, it is not 
so \ Some of his expectations, however, are neither grati- 



HOW WE COME TO BELIEVE IN IT. 231 

fied immediately nor finally disappointed, but only delayed. 
If he smells something good to eat he may have to wait 
before he can get it or even see it. But everything that he 
does in the interval is done with the anticipated experience 
in mind, and thus his activity takes the form of a search. 

Thus a period of delay between two connected experi- 
ences produces a modification in the original association. 
It is now no longer a matter of smell and sight or taste, but 
of smell, expectation and search, and then sight or taste. 
Moreover, the period of expectation and search is sometimes 
longer and sometimes shorter, and consequently if the child 
had to go away some day without finding the object of his 
search he would still think of it as there and picture himself 
finding it at the end of a longer search; so that at last he 
might say to himself, ' When you get the smell (or other 
sign, whatever it is) you can always find the object if you 
look long enough '. In some such way as this we come to 
believe that a uniform connection between two given cir- 
cumstances exists whether we happen to observe it or not. 
The same sort of experience taking place in a thousand other 
relations, we learn with each one of them to look for the 
circumstance that is necessary to fulfil our spontaneous 
expectations, or, in other words, to look for the relations of 
things necessary to make our experience of the world 
uniform. 

In cases where our expectations are not only delayed but 
positively disappointed, the disappointment or surprise is 
apt to prick our attention and miake us notice the presence 
of some variation in the conditions that we had not observed 
at first ; and if this circumstance happens to be connected in 
any real way with our disappointment and the experience 
is repeated, we soon learn to modify our expectations and 
to say ' When A is present expect B, except when C is present 
also '. In this way our expectations of uniformity become 
more and more refined. Moreover, since the feeling of sur- 
prise is present in every case of disappointed expectations, if 



2 2,2 THE UNIFORMITY OF NATURE. 

the feeling once makes us open our eyes and look around 
for the relation necessary to make our experience uniform and 
if the search proves useful, we shall be more likely to look 
around the next time we are surprised ; and thus form the 
general habit of seeking for uniformities when they are not 
apparent. 

Even this habit of seeking for uniformities in all the situa- 
tions in which we are placed is something different from a 
formal conviction that Nature is always uniform, just as the 
habit of meeting one's obligations is different from any 
theory that he should be honest; but for practical purposes 
the habit without the theory is better than the theory without 
the habit. The habit alone is sufficient to give the practical 
confidence in uniformity with which induction starts. When 
the logician asks the man of sound sense and practical use- 
fulness what reason he has for believing that the uniformity 
he looks for is always present the answer will probably not 
satisfy the logician. The man has never tried to give his 
habit of thought a logical basis; perhaps he has hardly 
recognized that he had it. It was merely one of the uncon- 
scious products of his nature that happened to help keep 
him alive. Yet, after all, when the general truth that Nature 
is always uniform does dawn upon us and does become 
explicitly recognized, it is through the habit. For if the 
question of the uniformity of Nature is ever put to us in this 
general way, we try to think of some situation in which we 
should not or could not feel the impulse to seek uniformity 
whether we actually found it or not, and when we cannot 
think of any we agree that uniformity is always to be sought; 
and this implies that it always exists. 

There is nothing in the world but a vast number of things 
of various kinds acting upon each other in various ways 
under various circumstances, and we cannot 
main possibly conceive of an event which could not 

aspec s. ^^ explained, if we knew enough about it, as due 

to the action of a thing or things of some particular kind 



ITS TWO MAIN ASPECTS. 233 

under some particular kind of circumstance. This is only 
another way of saying that the uniformities we expect to find 
in the world take two main aspects, one of which is indicated 
by the term ' thing ' and the other by the term ' circum- 
stance '. 

This distinction we make between things and circumstances 
enables us to find uniformity in phenomena even when they 
are not precisely alike. If the same series of phenomena 
should persist or recur with absolutely no variation, like the 
notes in a piece of music reeled off by a machine, the dis- 
tinction between things and circumstances would not be 
necessary; each part would be determined in every respect 
by its relation to the inflexible whole, and there would be 
no other particular part to which it bore any special relation. 
But, as our experience actually occurs, this is not the case. 
Experience is capable of infinite variation, and still it can be 
reduced to uniformity of the sort that we believe in by dis- 
tinguishing between these two aspects, the thing-aspect and 
the circumstance-aspect, and by supposing that either the 
thing or the circumstance can be changed while the other 
remains the same, or that both can be changed or remain 
the same together. In this way our belief in uniformity does 
not require us to expect an absolute repetition of events 
except when things and circumstances are both the same. 

To explain first of all what we mean by the thing-aspect 
of uniformity. We distinguish between different things, and 
therefore this thing-aspect of uniformity does not mean that 
all things are alike. For if everything in the world were to 
appear and act precisely like everything else no one would 
be able to distinguish his hat from the cat or a bar of soap, 
and there would be no reason why he should. On the other 
hand, if everything in the world were not only to appear 
different and act differently from everything else, but were 
also to be continually changing its appearance and mode of 
acting in a perfectly arbitrary way, it would still be impossi- 
ble to distinguish between one thing and another, for the 



^34 THE UNIFORMITY OF NATURE. 

points of difference found at one moment would cease to 
exist in the next. In the first case any expectation would 
be fulfilled by one thing as well as by any other; in this 
latter gase no expectation would be fulfilled by anything. 
Thus while the possibility of distinguishing between things 
implies that they differ from each other, it also implies that 
each of the things distinguished has some characteristic 
uniformity of appearance or way of acting which marks or 
constitutes its own individuality or nature. 

An oxygen atom acts in one way in the presence of 
hydrogen and in another in the presence of nitrogen, but it 
never ceases to act like oxygen and begins to act like iron 
or chlorine. A formula which told the various ways in which 
it does act under all possible circumstances w^ould be a 
definition of its nature. 

We not only assume that every thing has a nature of its 
own, but we assume also that there are absolute similarities 
between them, so that they can be divided into various 
' kinds ', all the things of a given kind having so much the 
same ' nature ' that one might be substituted for another 
without producing any perceptible change in the result. 

Along with the uniformities characteristic of certain indi- 
viduals and classes of things we come to have also some idea 
of the uniformities characteristic of things in general, partic- 
ularly of material things. A material thing, as contrasted 
with a mere phantasm, is expected to be tangible, to resist 
pressure more or less, to have a continuous existence in time 
and space in the sense of not passing from one point to 
another without passing through all the intermediate points; 
and perhaps also to obey the laws of inertia and gravitation. 
Finally, since things are only given as aspects of the sum 
total of experience called the world as a whole, by reference 
to which aspects the essential uniformity of the whole can 
be conceived, it is a part of the very nature of a thing to be 
bound up with others in a whole world, to act upon them 
and to be acted upon by them, and to observe the same 



ITS TWO MAIN ASPECTS. 235 

general laws. To speak of a thing out of all relations to 
everything else is to speak of an aspect apart from that whose 
aspect it is, and is therefore absurd. 

By the Circumstances of a thing as contrasted with its 
nature we mean, not the general rule of its action, but the 
particular conditions to which the rule must be adapted at 
any given instant. These conditions include the present or 
vanishing state or activity of the thing itself. An iron, for 
example, that has just been heated will not act precisely like 
one that has not. They include also the position and 
nature, and present or vanishing states or acts, of other things. 
Oxygen does not act in the presence of hydrogen precisely 
as it acts in a vacuum, and it does not act in the presence 
of hot hydrogen precisely as it does in the presence of cold. 

When I say that the conditions which help to determine 
an act include the position and state of other things besides 
the agent, I mean, not merely that sometimes an act is 
determined in part by something outside of the agent, but 
that it is always. The moth in its chrysalis seems to develop 
wholly from within, shut off from all the rest of the world; 
but take away the warmth of the sun outside and how long 
would the development last ? Even within the chrysalis we 
have not one simple thing moving by a wholly inward law 
from one state to another, as we may be inclined to assume 
at first, but rather a whole system of cells acting and re- 
acting upon each other; and each one of these cells again 
is composed of atoms, all acting with reference to what lies 
beyond them. In short, all explanations in natural science 
come down finally to atoms; and no explanation assumes 
that an atom ever acts wholly from within, regardless of the 
rest of the world. Therefore every ultimate explanation is 
made on the assumption that every act or state of a thing is 
determined partly from without. In other words, causation 
always involves interaction.* 

^' This is quite as true in psychology as it is in physical science. 
When we ' explain ' a person's thought we either regard it as due to the 



236 THE UNIFORMITY OF NATURE. 

Circumstances, like things, can be divided into various 
* kinds ' ; but in their case the division is always rather loose. 
Two things can be absolutely alike in their nature, for there 
is no reason why they cannot both act according to precisely 
the same general law. Bat two circumstances can never be 
precisely alike. If one exists here at this time the other must 
exist somewhere else or at some other time, and conse- 
quently they must always differ in time or place if in nothing 
else.'* We often speak of two circumstances being exactly 
alike, but when we do so we only mean that they are alike 
in every respect that is worth considering for the purpose in 
hand. Circumstances of essentially the same kind, like 
things of the same kind, can be substituted for each other 
without any essential change in the resulting phenomena. 
If they could not, the division of experience into the two 
aspects of things and circumstances would not help us in our 
conception of its uniformity. Wind blowing upon the green 
leaves of an aspen-tree here to-day makes them move here 
and to-day, if every other circumstance is the same, just as 
wind blowing upon them there and yesterday made them 
move there and yesterday. 

play of different feelings and ideas or else we turn to physiology and 
regard it as due to various ' currents ' in the cells and fibres of the brain. 
In either case the explanation involves something beyond what is ex- 
plained. Of course this causal analysis does not prevent us from believ- 
ing in the real unity of the mind, and a similar analysis in natural sci- 
ence does not prevent us from believing in the unity of the world. The 
fact that explanations take account of aspects of reality does not turn 
these aspects into something independent and self-existent. 

*I do not refer to their absolute position in time and space, — to mere 
position apart altogether from the relation of events to other events that 
precede or coexist with them and of things to other things that surround 
them. Such absolute position does not enter into our explanations at 
all, and is therefore not a ' circumstance ' in the sense in which the word 
is used here. When we say that the result of an act was different in two 
different cases because the act occurred at two different times it is not 
the bare time as such that we have in mind, but the preceding or con- 
current events; and the same is true. ??mtatis mutandis^ of differences in 
place* 



LAW. 237 

Having divided our world into these two aspects of thing 
and circumstance we are not satisfied to say merely that 
under precisely similar circumstances precisely 
similar things will produce precisely similar 
results. We go further, and seek for laws, which take 
account of the differences between things and circumstances 
as well as of their resemblances, and which tell not merely 
what takes place when the same things or precisely similar 
things are placed in precisely similar circumstances, but tell 
also how much variation in the circumstances or the things 
produces a given amount of variation in the result. We do 
not merely say that bodies attract each other; but we say 
that they attract each other in direct proportion to their mass 
and in inverse proportion to the square of their distance. 
This would not be possible unless we took account of the 
amount of difference between two situations and measured 
off one against another. It is this recognition of differences 
in amounts of difference, and their precise measurement, 
that enables us to introduce the conception of proportion 
into our formulae and to deal with them by mathematics. 

The notion of law would be impossible and our search 
for uniformity in the world would be doomed to failure if 
our ability to see different aspects of reality wxre limited to 
the general distinction between things and circumstances. 
But the very ability to enumerate a thing's different attri- 
butes involves the power on our part of attending to one of 
them at a time, and in the same way the very possibility of 
stating some general law such as that of gravitation involves 
the power of attending to some one of a thing's relations 
and accounting for it without saying anything about the rest. 
In accounting for the fall of an apple by this law, we con- 
sider its mass and the mass of the earth, its motion towards 
the earth, and the original distance between them. We do 
not say anything about its taste or color or even perhaps 
about its size and shape and its motion around the sun. Of 
course these neglected relations must be accounted for too, 



2 7,8 THE UNIFORMITY OF NATURE. 

and the state of affairs that produces them must be compati- 
ble with the state of affairs that produces the apple's fall. 
The total state of the world at every instant is the cause of 
its total state at the next; but we feel that we have a right 
in our explanations to break up this complex whole of each 
instant into as many aspects or different relations as we 
please and account for some of them at a time. 

Thus the uniformity discovered by each one of our explana- 
tions is a uniformity in some one definite respect, and when 
we speak of the ' Cause ' of an event we are almost always 
trying to pick out the essential elements of its nature and 
the relations to its own past and to other things that account 
for some few of its salient features. Nothing short of the 
whole universe would account for the event as an absolutely 
complete whole. 

The ability of which we have just spoken to attend to 

some one aspect of a situation involves certain dangers. 

For we may forget that the situation has other 
Precision i • i • i i i i r ■, 

in _ ^ aspects which might also be accounted for, and 

therefore rest with the feeling that our explana- 
tion of the situation as a whole is complete when it is really 
very incomplete. Worse still, the explanation which we give 
of the aspect of the situation that we happened to notice 
may be quite inconsistent with any reasonable explanation 
of the other aspects that we did not happen to notice, and 
therefore wrong, without our detecting the fact, as we should 
have done if we had realized how much there was to explain. 
We may say that the light on the wall comes through a 
certain window, and be perfectly sa.tisfied with the explana- 
tion so long as we fail to notice that the glass in the window 
is blue and the light on the wall is not. 

Nay, even if we notice such a discrepancy, we may delib- 
erately disregard it, with the feeling that in some way or other 
it can be detached from the rest of the phenomenon, and 
therefore makes no difference, and that in any case it must 
not be allowed to interfere with the conclusion already 



PRECISION IN UNIFORMITY. 239 

reached. This is more likely to be true when our emotions 
are involved. If a storekeeper has been robbed and there 
are five or six impressive circumstances which all suggest a 
certain clerk as the culprit, he may jump to the conclusion 
that the clerk is guilty, although he is perfectly aware of 
some other circumstance, which is less striking, but which 
is nevertheless absolutely incompatible wdth the clerk's guilt. 
If this circumstance is mentioned and the storekeeper is 
forced by it to admit that the clerk is not guilty there is 
considerable chance that he w^ill admdt it very reluctantly, 
and will still feel that he ' nearly did it', and bear him a 
grudge accordingly. The good reasoner, whether he be a 
scout finding a trail, a detective tracing a crime, a physician 
diagnosing a case, or a scientist pure and simple, is the one 
who has not only skill enough to observe the less striking 
circumstance but strength enough to hold it in mind until it 
is accounted for, instead of allowing it to be swept away like 
the still small voice oi conscience by the larger mass of more 
vigorous impressions and associations that hurry us on to a 
more apparent goal. 

Even in the aspect of a situation that we really do attend 
to we may overlook the necessity for explaining the finer 
details. Every one knows in a general way that rough water 
is caused by wind; but when we have accounted for this 
general appearance of roughness most of us are satisfied. 
As Professor Huxley says: "Even thoughtful men receive 
with surprise the suggestion" that the form of every wave 
and the direction taken by every particle of foam " are the 
exact effects of definite causes "; and so long as w^e fail to 
recognize this precision of the causal relation it is perfectly 
evident that we do not realize the complete uniformity of 
nature. 

Thus while it is absolutely necessary that we should ignore 
certain aspects of a situation when we try to explain others, 
it is quite as necessary that we should not ignore the wrong 
ones. The only thing to do under these circumstances is 



240 THE UNIFORMITY OF NATURE. 

first to make an explanation that will account for the aspect 
of the situation in which we are interested and then to 
inquire in a cold-blooded, critical way whether there are not 
other aspects of the situation with which the explanation is 
not consistent. If there are we must reject it even though 
it has cost us years of labor. It may be that every one has 
a lurking tendency to feel that a plausible explanation has 
some value, whether it be true or not, until it is proved to 
be false. But — except as it helps us to remember the facts 
themselves — it has not, and the sooner we recognize its 
falseness and try to find one that will stand in spite of criti- 
cism, the better it is for ourselves and everybody else. It is 
useless to try and live in a fool's paradise or to bury our 
heads in the sand and refuse to recognize the disagreeable 
facts that upset our theories. 

Besides the necessity for looking at one aspect of a situa- 
tion at a time there is another reason why it is hard to realize 
that every event "is the exact effect of definite causes''; 
namely, because it is hard to realize that the events them- 
selves are exact and definite. Most of our ideas are very 
hazy, and it takes hard training to make us realize that the 
realities which these ideas profess to represent are not as 
hazy as the ideas themselves; that though we can form no 
clear idea of the beginning of things, there was no chaos, no 
mere 'stuff' without definite attributes and relations; and 
that though we may be in doubt about some state of affairs, 
there is no uncertainty or hesitation in the state of affairs 
itself. Hazy thoughts claim to represent reality as much as 
clear ones, and so long as all our thoughts are hazy we 
cannot realize that the claim is false. We must know some 
things definitely before we can begin to realize that all things 
are definite whether we know them definitely or not. 
Whenever we have used exact measurements so often that 
we feel the tendency to apply them to everything and no 
description seems complete without accurate statements 
about size, shape, direction, number^ duration, degree, and 



THE THING-ASPECT OF THIS PRECISION. 241 

so on, we are then in a position to realize that these quanti- 
tative relations of things fit into the general lavv^ of uniformity 
as well as the qualitative. Then, but hardly any sooner, do 
we realize that the form of every wave and the path of every 
falling leaf are ' the exact effects of definite causes ' ; that 
the law of uniformity is not only universal but precise. 

To realize the uniformity of nature it is quite as necessary 
to keep a clear view of the individuality or separateness of 
different things as to make clear distinctions 

between different circumstances. Yet this abso- JA^ „ . 

tnin^-aspect 

lute distinction between different things we often of this 

^ precision. 

tend in our instinctive reactions to ignore. If 
we are stung by one hornet it seems appropriate in revenge 
to wipe out the entire nestful, whether it includes the one 
that hurt us or not. If certain Americans are massacred by 
a set of Chinamen in Asia it is perfectly natural for a mob 
of other Americans to revenge itself by attacking some inno- 
cent laundryman in Kansas City. If two or three members 
of a household do us an injury it is difficult, especially if we 
are not brought into close contact with them, not to harbor 
resentment against the whole household. To the individuals 
themselves the difference between them may mean everything; 
to us it means nothing at all. 

In much the same way as we ignore the numerical differ- 
ence between several individuals and treat one as though in 
some way it were actually identical with another because it 
belongs to the same group, so we ignore also the distinction 
between different kinds of individuals. To make an accurate 
definition is one of the hardest things in the world; but the 
curious thing is that it often comes to people as a sort of 
revelation that such definitions can be made at all. * Defini- 
tion is possible ! ' This thought it was, perhaps more than 
any other, which gave Socrates a life-long inspiration. But 
to assert the possibility of definition — to say that some 
moral attribute or some material thing can be defined in such 
a way as to include by the very definition all that we think 



242 THE UNIFORMITY OF NATURE. 

the word should stand for, and to exclude all that we think 
it should not — is only another way of saying that whether 
we can find it or not the difference between things or kinds 
of things is always perfectly definite. 

In still another way uniformity of nature involves more 
about things than is evident at first. It involves the abso- 
lute permanence of whatever can truly be called a Thing. 
People often suppose that when things are ' burned up ' the 
total amount of matter or of ultimate things in the world is 
diminished and that when plants grow it is increased. But 
such a supposition is inconsistent with the very idea of a 
thing and with all our explanations of events that involve it. 
When we say that some given event is due to the circum- 
stances in which certain things were placed, we take it for 
granted that the things existed before the circumstances, and 
were thus at least relatively permanent; and when we learn 
that the permanence of sticks and stones and other such 
things by which we have explained events is not absolute, 
we account for it by saying that after all they are not really 
things at all in the ultimate sense of the word, but only 
temporary combinations of atoms, which latter are truly per- 
manent ; and that these atoms are the true things. Thus 
we come to realize what the scientists call the conservation 
of matter. The permanence of things is one of the two great 
aspects under which we think of the general law of uni- 
formity in the world; and to assume that any real thing is 
not permanent is therefore to deny the existence of absolute 
uniformity. Yet it is difficult to realize in a positive way 
that the law of uniformity implies the absolute permanence 
of every ultimate 'thing'. This scientific principle of the 
conservation of matter (and of any other ultimate reality) 
states for the things involved the same absolute uniformity 
that the law of absolutely precise causation states for the 
circumstances in which they are placed. 

Thus far we have explained how we grow into the belief 
that Nature is uniform, and we have shown the forms which 



PROOF OF UNIFORMITY. ^43 

we expect that uniformity to take; and yet after all we have 
not proved that such uniformity exists, and it is the pi-oof of 
proof of facts and not the history of beliefs with uniformity. 
which we are concerned i-n logic. But where would such proof 
begin ? If we do not take uniformity of any sort for granted 
we should have to begin like Descartes by pretending to doubt 
our own existence and the existence of other people to w^hom 
the proof might be addressed, for even personal identity is a 
principle of uniformity; and we should assuredly share in 
Descartes' failure. If, on the other hand, we are willing to 
be less thoroughgoing than Descartes and take something for 
granted to begin with, and thus begin our attempted demon- 
stration wdth the assumption that there are things and that 
various uniformities have existed in the past, why is this 
any evidence that other kinds of uniformity exist now or 
that any whatever wall exist m the future, — unless we already 
take for granted some wider principle of uniformity which 
decrees that if uniformity exists anywhere or at any time it 
must exist everywhere and always ? The fact that the sun 
has risen (as we believe) every twenty-four hours throughout 
long ages makes us expect that it will rise to-morrow; but 
unless we already assume that the future will resemble the 
past it does not prove it. 

Possibly the best thing that any one can say in justifica- 
tion of his conviction that experience depends upon a world 
of uniform relations is merely this : that it is a faith growing 
out of his very nature as an active being (if he exists and 
has a nature), that he has lived by it in the past (if he has 
had a past), that the longer he has taken it for granted the 
more it has seemed to justify itself, and that he means to 
take it for granted in the future (if there is a future). Our 
belief in the uniformity of things is thus something which 
we can account for psychologically, and we can show that 
to deny this uniformity in toto involves conclusions which no 
sane man is walling to act upon ; but there is no direct way 
of proving its existence. 



CHAPTER XXIII. 

SCIENCE AND THE PECULIARITIES OF THE RELATIONS 

THAT IT TRACES. 

The conviction that there is a distinction between circum- 
stances and things is only a starting-point in our search for 
the uniformity that we believe to pervade the 
work of world. The vast differences between one com- 

SCi6ILC6* 

plex group of phenomena and another are not 
explained to our satisfaction by the mere general statement 
that they are all due to differences between things and the 
circumstances in which they are placed. The difference 
betw^een one complex situation and another is always per- 
fectly definite, and what we want to find out is the precise 
difference in the things and in the circumstances that 
accounts for this definite difference in the situations as a 
whole. This is the business of Science, and its work has 
two sides: (i) Observing as much as we can, and finding 
out from what we observe the general laws according to 
which things always act; and (2) inferring further from the 
concrete combination of circumstances or events that we 
observe and from the general laws that we have discovered 
what must be the concrete state of affairs where we cannot, 
or cannot yet, observe. As a result of various concrete 
observations made by himself and others Newton discovered 
and proved the law of gravitation; and an astronomer who 
knows this law and also observes the position of some 
heavenly body at various intervals is able to tell where it was 
before he saw it, when it will come within a certain distance 

244 



INDIVIDUAL IDENTITY AND CAUSATION. ^4^ 

of the earth or the sun, and what will happen to it and to 

them when it does. In this way any one who was master 

of an absolutely perfect science would be able (i) to find 

every law in the universe, and then (2) starting with the 

present, to go back indefinitely and tell the history of the 

past and to look forward just as far and tell the story of the 

future. In the following chapters we shall speak first of the 

logical method pursued by scientists in the discovery of 

general laws, and afterwards of the application of these laws 

for the discovery of particular concrete facts. But before 

we begin it is desirable to say a few words more about the 

nature of the identity and causal interaction assumed in all 

such investigations. 

To tell whether one object resembles another we need only 

look at the two and compare them, and in the same way we 

can often tell by direct observation whether one 

event succeeds another: but to tell whether one Peculiarities 
..,.,., , , , of individual 

object IS identical with another, or whether some identity 

given event is the cause of another, simple interaction. 
inspection is not sufficient. If we lose sight of 
a thing for a single instant how can we tell that it has not 
been removed and another put in its place ? Indeed, until 
we know something more about it than its outward appear- 
ance, how can we even be sure that such a substitution has 
not taken place by some jugglery before our very eyes ? So 
also with the causal relation between one thing and another; 
however certain we may be that a change we observe in one 
thing followed immediately after a change we observed in 
something else, how can we be sure that it was caused by 
this rather than by a change in some third thing, miles away 
perhaps, that we did not happen to observe at all ? No one 
can directly observe either the identity of an object with 
itself or its causal action upon something else, and therefore 
our identifications and causal explanations have to be reached 
by guesswork in the first instance, and if they are afterwards 
proved to be correct the proof has to be indirect. 



246 SCIENCE AND THE RELATION IT TRACES. 

Another thing to notice about these relations of identity 
and causal interaction is the conviction we feel that they are 
always present. Since they are aspects of the uniformity of 
nature that we believe in, we have a right to believe that at 
every moment in the past there were things identical wdth 
the things of the present, and that there are and always have 
been causal relations to other things that help to explain 
their present conditions; and the same is true, mutatis mutan- 
dis, of the future. 

Still another peculiarity of these two relations is their 
exclusiveness. In this respect identity and causal interaction 
are very different from resemblance and succession. The 
house I live in can be similar to each one of a hundred 
others, wholly regardless of the place and time of their exist- 
ence, and its similarity to one does not interfere in the 
slightest with its similarity to some other. It is true too 
that the house that keeps out the rain to-day can be identical 
with the house that was bathed in sunshine yesterday and 
none the less identical on that account with the house that 
was covered with snow two months ago, for these relations 
of identity and causation go back from instant to instant 
without a break to all eternity; but the house cannot be 
identical with one existing in some other place or state at 
the same time. There is only one thing at a time with which 
it can be identical, and to be identical with this means not 
to be identical with some other. The same exclusiveness is 
found also in the case of causation. The house we have 
been talking about can exist at the same time as an unlimited 
number of others, and an unlimited number of things might 
have been acting before or during its erection; but if the 
house was built by John Smith it could not have been built 
by anybody else; and if a spark from a certain locomotive 
destroyed it, it is quite certain that an earthquake or a stroke 
of lightning did not. It is perfectly true, to be sure, that if 
we try to explain absolutely everything about the house as it 
exists at a given instant the explanation will have to include 



INDIVIDUAL IDENTITY AND CAUSATION. 247 

a statement about absolutely everything in the universe the 
instant before. Thus, inasmuch as the position in space of 
every object depends upon that of every other, the position 
of the house would certainly be affected by a boy throwing 
a stone in China. And if we use the word ' cause ' with refer- 
ence to some single aspect or relation of things that we are 
trying to explain it is true also that even this single relation 
may be due to the co-operation of several causes. John 
Smith may not have built the house alone. But when causes 
co-operate in this way no one of them is a complete cause. 
If anything is the complete cause of a condition, so far at 
least as one instant of time is concerned, it is its sole cause. 
A resemblance or coexistence or succession can belong at 
once to many things without diminishing the share of any. 
A relation of identity or causal interaction can not. 

Our knowledge, or rather our assumption, that these rela- 
tions of individual identity and causal interaction always 
exist and are always exclusive is very helpful in our search 
for uniformity in nature. If we have any way of showing 
that this, that, and the other thing of one instant is not 
identical with the thing of another, the first of these assump- 
tions gives us a right to infer that some other — perhaps the 
only one left — is. In the same way, if we have any means 
of showing that this, that, and the other thing had nothing 
to do with some present condition of a thing that we are 
inquiring about, our assumption gives us the right to infer 
that something else had. In this way we can apply the 
' method of exhaustion ' in our search for particular uni- 
formities. So with the second assumption, if we know that 
this thing of one instant is identical with a given thing of 
another, we know perfectly well that w^e need not look for 
any other thing of the same instant to be identical with it. 
Here again the same is true, mutatis mutandis, of causation. 
In this way our search for uniformity is simplified and 
shortened. 

The fact that causes may be endlessly complex gives one 



248 SCIENCE AND THE RELATION IT TRACES. 

of our two relations — that of causal interaction — still another 
peculiarity, which is very important. The relatively simple 
relations between two or more things that we are accustomed 
to pick out and call relations of cause and effect are not 
independent; for the sequence of what we call the ' effect ' 
upon what we call the ' cause ' is at the mercy of other 
causal relations. If two things are similar their similarity is 
neither increased nor diminished by their likeness to other 
things or by the likeness of other things to each other. John 
does not look any the less like James because he looks like 
Henry also, or because Henry looks like Thomas. In the 
same way, if the line AB meets the line AC at an angle of 
45 degrees you can draw as many more lines as you like to 
the point A from as many different directions as you like, 
without affecting the size of the angle in the slightest. As a 
result of this we are justified in absolutely ignoring the exist- 
ence of Henry when we are discussing the resemblance of 
John and James, and in ignoring all the other lines which 
meet at A when discussing the relations of AB and AC. 

This possibility of considering tw^o relations regardless of 
everything else in the world is what makes the problems of 
deduction and of geometry so relatively simple. But with 
causation all this is changed. John can beat James in a 
fight if they are left alone, but if Thomas warns James to run 
or takes part too he cannot; the sun will keep a comet in a 
certain path if they are left alone, but if Jupiter happens to 
come too near, the comet may swing out of its path; and 
so on. Whether A is similar to B is a mere question between 
A and B; but whether A will cause B to act in a certain way 
is a question that also involves C and D and E; and when 
we are trying to find out what A will make B do we must 
know whether C and D and E are present and how they are 
acting. We cannot ignore them. If they are not affecting 
the relations of A and B we must make sure that they are 
not; and this, of course, makes our problem much more 
complex. Deduction and geometry can neglect irrelevant 



INDIVIDUAL IDENTITY AND CAUSATION. 249 

circumstances; inductive reasoning about relations of cause 
and effect must eliminate them. This is often very difficult; 
and when the elimination has been made and we are thus 
able to conclude from the cases examined that A's action 
was the cause of B's, wx must not conclude from this that 
this same act on A's part w^ill always be followed by the 
same act on B's; but only that such wdll ahvays be the case 
as long as nothing else interferes.* 

This fact that one cause can interfere wath another is what 
makes a knowledge of causal relations so very important 
practically as well as theoretically. No human effort can 
change a thing's identity, but if we know^ enough we can 
use our bodies in such a w^ay as to pit one cause in the w^orld 
against another and change its effects in accordance wdth 
our purposes. This is why knowledge is power. The thing 
that makes the knowledge of causal relations most difficult 
is the very thing that makes it useful. 

* In this connection the reader may recall the statement made on p. 80 
that causal relations seem to penetrate into the very being of things, 
while non-dynamic relations exist only externally for some observer. In 
this respect identity is like causation. 



CHAPTER XXIV. 

THE METHOD OF EXHAUSTION AND THE SEARCH FOR 
PARTICULAR UNIFORMITIES. 

We use the method of exhaustion when we base a conclu- 
sion upon the results of a more or less direct and serious 
attempt to examine every case of a given sort in the universe. 

The simplest application of this principle is found in the 
so-called Aristotelian, or Perfect, Induction. The first ex- 
ample of induction given on page 224 was of this 
inductioko' ^^^^' namely : This, that, and the other member 
of a certain family each has light hair; these 
members constitute the whole family; therefore every mem- 
ber of the family has light hair. In the same way we can 
say : ' The apostle James was a Jew ; so was John ; so was 
Peter ' ; and so on through the twelve; ' therefore the twelve 
apostles were all Jews '. January contains less than thirty- 
two days; so do February, March, etc.; therefore each 
month of the year contains less than thirty-two days. In 
this ' perfect induction ' the conclusion is something more 
than a mere summary of the particular facts stated in the 
premises; for we might know that James was a Jew and that 
John was a Jew, and so on through the twelve, without 
knowing or without thinking that these twelve were all the 
apostles. 

This Perfect Induction is relatively rare; for it is only in 
comparatively few cases that we can be sure that the indi- 
viduals named constitute the whole class in question. 

250 



PERFECT INDUCTION. 251 

" The assertion that all the months of the year are of less 
length than thirty-two days ... is a certain conclusion 
because the calendar is a human institution, so that we can 
know beyond doubt how many months there are. . . . But 
the assertion that all the planets move in one direction round 
the sun, from West to East, is derived from Imperfect 
Induction; for it is possible that there exist planets more 
distant than the most distant known planet Neptune, and " 
of " such a planet of course the assertion would '' not hold 
true.* 

If a being who was purely rational found that a Perfect 
Induction was impossible, he might go no further. But we 
men are animals as well as rational, and have an -^j^y^g 
animal's tendency to react to every impression, accept less. 
and to react in the same way when the impressions are 
similar. Consequently we will often risk a conclusion that 
the premises will not altogether warrant, and when all the 
individuals with a given general appearance that we have 
examined have a certain particular characteristic we almost 
always take it for granted that those we have not examined 
have it also. " Practically in inductive argument an 
opponent'' who maintains that some general statement is 
not true " is worsted when he cannot produce an instance 
to the contrary. Suppose he admits the predicate in ques- 
tion to be true of this, that, and the other, but denies that 
this, that, and the other constitute the whole class in ques- 
tion, he is defeated in common judgment if he cannot 
instance a member of the class about which the predicate 
does not hold. Hence this mode of induction becomes 
technically known as Inductio per enumeratioftem snnplicem 
uhi non repe7'itur instantia contradicioria. When this phrase 
is applied to a generalization of fact, Nature or Experience 
is put figuratively in the position of a Respondent unable to 
contradict the inquirer.'' \ 

Thus we see how the inductive process by which we make 
* JevoDs' "Lessons", p. 213. \ Minto, pp. 236-7. 



252 THE METHOD OF EXHAUSTION. 

and try to justify a universal proposition falls short of its 

ideal. We set out to exhaust the universe, and 
practicai!^^^ stop when we have exhausted our own knowledge 

or when we get tired of going any further, but 
we draw our conclusion nevertheless. The only justification 
we can give for such a proceeding is practical ; that on the 
w^hole we get along better if we jump to such conclusions 
after a reasonable amount of investigation than if we always 
suspend our judgment and refuse to act until our data are 
absolutely complete. 

How many cases constitute a ' reasonable ' number upon 
which to base a general conclusion depends altogether upon 

circumstances. If the general conclusion in 
we gues^? question fits in with what we know about other 

things it will not usually require so much evi- 
dence in its favor as it would if it did not. In view of what 
everybody knows about other animals it requires very little 
evidence to prove that all sheep are mortal. How many 
cases make a reasonable number depends too upon how likely 
it is that we should know of an exception to the general rule 
if one existed. That every man in the civilized world is less 
than twenty feet tall we have a right to say at once, because 
we know that if taller men than that existed anywhere within 
the bounds of civilization we should be sure to have heard 
of them. A third consideration which helps to determine 
how many cases we should investigate before venturing upon 
a general statement is the practical importance of the ques- 
tion at issue. If the eternal- salvation of every human being 
depended upon the truth of our statement the number of 
cases investigated would have to be very great indeed before 
any one of us would think it reasonable to draw the general 
conclusion. Anything short of an absolute exhaustion of 
the group in question fails to give absolute certainty, and 
the completeness of the exhaustion which we feel compelled 
to make will always depend upon the amount of certainty 
that v/e require, 



HOW PROBLEMS AND RELATIONS ARE INTERWOVEN. 253 

Though the circumstances which help to determine how 
much evidence for a general conclusion is reasonable are 
related to the case in question, they all lie outside of it. 
That is to say, the question of how much evidence is reason- 
able does not depend so much upon the nature of the 
problem in itself as upon its relation to what we know about 
other things — e.g., the constitution of society that makes 
it likely that we should hear of a man twenty feet tall if he 
existed, the supposed divine law that would lead to our 
damnation for a false guess, etc. 

The one thing in this connection which the student of 
logic should not overlook is this: As civilization advances, 
the need for accuracy and certainty of thought and action 
constantly increases. Our environment in this respect is 
changing very rapidly, while our natures change very slowly. 
The consequence is that the average man is apt to be too 
impatient of suspense and to jump to his conclusions too 
rapidly for his own good. And if the individual happens to 
be concerned with science, in the very front of the forward 
movement, where the need for accuracy and the means of 
attaining it are growing most rapidly, then intellectual 
patience becomes a virtue of which he can hardly have too 
much. An incautious or inaccurate farmer may get along 
after a fashion even in this day; but an inaccurate scientist 
is almost certainly bound to be an utter failure. 

Perfect Induction and the Inductio per Enumerationem 
Simplicem may be regarded as the inductive processes corre- 
sponding to the first figure of the syllogism. 
They are not concerned pre-eminently with any proWems 
particular kind of relations; they involve no tionsare 
refined analysis; and their only positive charac- 
teristic is the generality of their conclusions. 

On page 225 we saw how the principle of exhaustion is 
used to ascertain relations of identity and causation as well as 
to prove propositions that are merely general ; and how the 
principle therefore furnishes an inductive process correspond- 



254 THE METHOD OF EXHAUSTION. 

ing to each figure of the syllogism. In the case of the 
general proposition the method of exhaustion is one of addi- 
tion, — such and such a thing is true of this ajtd that and the 
other, therefore of all. In the case of identity and causation 
the method of exhaustion is one of subtraction or elimina- 
tion, — the thing or the cause in question cannot be this or 
that, therefore it must be the other. This method of elimi- 
nati<:>n would not be possible unless we were sure enough of 
the uniformity of nature to assume that a thing identical 
with the one in question or that a cause for the given event 
must surely exist somewhere. 

It is noteworthy that in practice questions concerning 
general truths, concerning identity and concerning causation 
are interwoven in many ways. When we have proved either 
by a ' perfect induction ' or by the Inductio per Enumera- 
tionem Simplicem that everything with the characteristic 
A has also the characteristic B we can hardly avoid suspect- 
ing that between A and B there is some rather direct relation 
of causation. Conversely we can prove that everything with 
the characteristic A has also the characteristic B without the 
Perfect Induction or Inductio per Enumerationem Simplicem 
if we have any means of proving that A inevitably causes B. 
So with Identity. A person can be sure that the book he 
finds in a certain library to-day is the one he left there 
yesterday if he can prove that it is the only book like his 
that is now in the library, and that no books have gone out 
and come in since his was left. But how can one be 
sure that a book has not gone out of the library and another 
come in to take its place '^. Is it not only because he knows 
that books cannot pass through solid walls or throw them- 
selves spontaneously through windows and doors, and 
because he knows also that if anybody had carried one book 
in and another out the librarian would have seen him or the 
lock on the door would have been broken, or some other 
perceptible change would have been caused, when it was 
not ? 



HOW PROBLEMS AND RELATIONS ARE INTERWOVEN. 255 

In this way knowledge of causal relations helps us to 
prove identity just as it may help us to prove the truth of a 
universal proposition. Such a case as this is not excep- 
tional. We prove that the comet now visible is the one that 
appeared ten years ago because calculations made at that 
time showed that at precisely this time it must appear at the 
very spot where a comet is now seen; and since there cannot 
be two comets in the same place the one we see now must 
be the one we saw then. So too when a ' medium ' tries 
to prove to you that the spirit with which she now claims 
to be in communication really is the spirit of your departed 
friend she tries to show that the spirit does and knows what 
nobody but that friend would or could do or know; and 
thus she leaves this problem on your hands: If my friend 
did not speak through the medium, how in the world am I 
to account for all the things the medium or the spirit that 
spoke through her did ? In the same way once more, when 
a prosecuting attorney tries to prove that the prisoner before 
the court was the person who broke into the bank he 
attempts to show that there is some effect which could not 
possibly have been produced if the burglary had been com- 
mitted by anybody else. Thus a question of identity, like 
the question of the truth of some general statement, can be 
Resolved into a question of causation. 

So, vice versa, when we are investigating a question of 
causation we always take for granted various relations of 
identity and various relations of kind such as are expressed 
in general propositions. When we conclude that a certain 
man must have been poisoned by arsenic because nothing 
else would have caused the same symptoms we assume the 
existence of the man and of the arsenic as real things retain- 
ing their identity from the timieof the supposed poisoning to 
the time that the symptoms appeared. We also assume that 
every bit of arsenic has the same nature as every other bit 
and acts in the same way under the same conditions, and 
that men also are similar to each other, so that at least some 



256 THE METHOD OF EXHAUSTION. 

of the symptoms produced by the arsenic are substantially 
alike in them all. 

In courts of law individuals as such are everything, and 
general laws or rules of action are only means for adjusting 
their conflicting claims. Consequently problems of identity 
in the courts are all-important, and all sorts of devices are 
resorted to for answering such questions as whether or not 
this particular man is the one that owned this particular 
horse or signed this particular bit of paper. But with science 
it is different ; for scientists have very much more to say about 
the conditions under which certain effects are produced than 
about the identity of the agents. Since the chemist assumes 
all atoms of hydrogen to be alike he neither knows nor cares 
whether the one involved in a given reaction is Atom No. 49 
or Atom No. 6^. His identification stops when he finds out 
that the atom in question is some one or other of the many 
billions of similar atoms that we call hydrogen, and that it 
has recently been put through such and such a process. 
For that particular atom as such he cares not a snap of his 
finger. Its only value for him is to show what any atom of 
the sort will do under a given set of conditions. This dis- 
tinction, however, is not absolute. The jury in a trial for 
murder has to determine whether the injury inflicted by the 
prisoner upon the deceased really was the cause of his death, 
and such sciences as geology and history are concerned very 
largely with the question of what individual person or thing 
it was that produced this or that given effect. After all, the 
question of identity and the question of circumstance are 
inextricably interwoven; for thing and circumstance are 
only different aspects of the same concrete fact and neither 
could act or even exist without the other. 



CHAPTER XXV. 

INDUCTION BY SIMPLE ENUMERATION AND THE SEARCH 

FOR CAUSES. 

The Inductio per Enumerationem Simplicem is regarded 
by scientists nowadays as a primitive and unsatisfactory 
kind of inference that should be replaced or sup- 
plemented wherever possible by an inference ^iference' 
based upon the knowledge of causes. The CvSsen- «ation^^^" 
tial difference between the two methods is that 
the one based upon a knowledge of causes involves analysis 
and the other does not. Inductio per Enumerationem Sim- 
plicem takes each of the observed relations in the mass just 
as it stands, notices how often they coincide, and then makes 
a guess about the future. Causal analysis is not content to 
take the observed uniformities so roughly ; but splits them 
up, in order to find the simpler and more general uniformi- 
ties which are involved. And then when this is done it may 
try to determine the conditions under which they will work 
together in the same way again. An inference based upon 
the knowledge of causes is therefore based upon a definite 
knowledge of all the details rather than upon a confused im- 
pression of a whole. 

A farmer may happen to notice that red clover grows 
better near the homes of old maids than elsewhere in the 
neighborhood. Reasoning per enumerationem simplicein he 
might conclude that there is always something about an old 
maid that helps the growth of clover. But he would have no 

257 



2S8 SIMPLE ENUMERATION AND CAUSAL ANALYSIS. 

means of knowing how much faith should be attached to this 
conclusion. He could not say how likely it was that the next 
case he noticed would conform to the rule. But suppose he 
should happen to think that old maids often keep cats^ that 
cats kill mice, that mice destroy bumblebees, and that with- 
out bumblebees to carry the pollen from one plant to another 
red clover cannot develop its seed. Then he would have 
broken up the first uniformity — between the old maids and 
the clover — into a series of others, most of which, at least, 
are much more familiar and therefore much more thoroughly 
tested; he would know almost exactly how much reliance could 
be placed upon each of them ; and putting them all together he 
could say without any hesitation whatever whether it is always 
true that old maids help the clover-meadows. In this way, a 
knowledge of causes gives much greater certainty than the 
bare, unanalytic Inductio per Enumerationem Simplicem. 

In this example, as in almost any other that might be 
given, the analysis into causes or simpler uniformities is very 
incomplete. Each of the causal relations given might be 
itself reduced to others still simpler. That old maids keep 
cats ; that cats kill and eat mice ; that mice destroy the nests 
and young of bumblebees; and that red clover needs these bees 
to fertilize it : all these may be themselves mere Inductiones 
per Enumerationem Simplicem, about which we may feel 
sceptical ; and we may wish to test any or all of them by 
finding the still simpler uniformities that would account for 
them if they really existed. If cats do always eat mice, the 
mice are probably good for them ; if mice are good for cats 
to eat, it must be because they can be digested and pass into 
the system ; if digested food passes into the system of a cat 
or any other animal, it must be because it can get through 
the membranes lining the alimentary canal ; if food can get 
through these membranes, it must be because certain fluids will 
pass through moist membranes anywhere. In this way one 
uniformity after another can be reduced to others still more 
general, until we can carry the process no further and we 



ANALYSIS AND CLEAR THINKING. 259 

have to content ourselves at last with certain simple laws of 
chemistry and physics. 

When any event is shown to have taken place in accordance 
with uniform laws, or when some uniformity is reduced to 
others more simple and more general it is said to be * ex- 
plained '. The simplest and most general laws of all must 
be accepted without explanation on the strength of an In- 
ductio per Enumerationem Simplicem. The most that we 
can say for the existence of any of them is that they seem to 
be involved by a vast number of experiences and to be con- 
tradicted by none.* 

When we find the causes back of any observed uniformity, 
the things with which we started become more fully known 
as well as the relations between them, and the 
knowledge of both things and relations in becom- and clear 
ing fuller becomes also clearer. In the example 
given ' red clover ' took a definite character as a plant depend- 
ent for its propagation upon cross-fertilization by an insect 
able to reach its nectar, and if we had asked why the pollen 
must be carried, why the bumblebee is better able to get at 
the nectar than other insects, and so on, we should have gained 
still clearer and fuller ideas about the clover. As the rela- 
tions with which we begin are not fully analyzed and ex- 
plained until they are reduced to ultimate laws, so the things 
with which we start are not completely understood until each 
of them is analyzed at last into a definite group of various 
kinds of atoms. 

The clearness and definiteness of thought which causal 
analysis gives is as valuable in itself as the greater certainty of 
inference that goes along with it. General appearances ob- 

■^ The sociologist, for example, cannot get along without assuming 
certain laws of mind ; the psychologist tries to account for mental laws 
by reference to nerve-physiology ; the physiologist tries to reduce his 
data to laws of chemistry and physics ; the chemist tries to explain his 
data by molecular physics; and the physicist tries to state all his facts 
in the formulae of mathematics. 



2 6o SIMPLE ENUMERATION AND CAUSAL ANALYSIS. 

scurely apprehended are often sufficient to call forth a fairly 
definite and appropriate reaction on our part. The lines on 
a companion's face may be quite indescribable by us and yet 
suggest the words ^ He is angry '. In the same way a number 
of very indescribable impressions may suggest the word^ Iron ' 
or ^Bewitched' or 'Tyrannizing'. These vague impres- 
sions are valuable because the words and other reactions to 
which they lead are generally fairly appropriate and useful. 
And yet real things and relations are never vague, and vague 
impressions can never represent them. They do not pre- 
cisely misrepresent them, for vague ideas neither represent 
nor misrepresent, since they cannot be measured against the 
facts at all. How can we ever prove that Mother Hubbard 
does not ' hoodoo ' her dog or ' project ' her thoughts in such 
a way as to ' impress ' the brain of the Czar, until we know 
precisely what it means to be ' hoodooed ' or what a ' pro- 
jected ' thought is supposed to do to the brain that it ' Im- 
presses '? Hence if one's expectations are only vague enough 
there is no such thing as definite fulfilment or definite dis- 
appointment. Definite conceptions, on the other hand, can 
represent realities ; and therefore there is some chance of 
having one that does. If it does not, its very definiteness 
makes it possible to prove that it does not. If it does, we can 
count upon it always. Thus a second reason for seeking to 
reduce observed uniformities to their causes is the clearness 
of conception which it gives. 



CHAPTER XXVI. 
THE METHODS OF DIFFERENCE AND AGREEMENT. 

In the preceding chapters we have discussed the general 

principles involved in inductive reasoning. We must now 

see how the principles are applied to various kinds 

.1 ^TT 1 111 Different 

of concrete problems. We have seen already that ways of ^ 

these problems may be divided roughly into two theuni- 
classes : the discovery or verifying of general 
laws, and the ascertaining of concrete individual facts. 
Questions of concrete fact will not be discussed until after 
we come to Chapter XXXIII. At present we shall consider 
only questions of general law. 

The principles involved in these questions are always the 
same, yet there are differences in the data to which they are 
applied which involve corresponding differences in the ap- 
plications ; and if our knowledge of the principles is to have 
any richness, we ought to know something about these differ- 
ent ways in which they are applied. The most striking appli- 
cations are to be found in scientific investigations. Many of 
these are described in Herschel's '' Discourse on the Study 
of Natural Philosophy" (1832) and in Whewell's tw^o large 
volumes on the '^ History of the Inductive Sciences " (1837) 
and his ^^ Philosophy of the Inductive Sciences" (1840), 
from which subsequent writers have drawn much of their 
material. With the facts and theories of these writers before 
him John Stuart Mill set out in his ^^ Logic" (published in 
1843) to ^generalize the modes of investigating truth and 

261 



262 THE METHODS OF DIFFERENCE AND AGREEMENT. 

estimating evidence, by which so many important and recon- 
dite laws of nature have, in the various sciences, been ag- 
gregated to the stock of human knowledge ', and Mill's 
chapter on ^^The P'our Methods of Experimental Inquiry" 
contains the classical account of the various ways in which 
the principle is applied for the discovery of causal relations.^ 
These different ways of applying the principle are called by 
Mill the Method of Agreement, the Method of Difference 
(including the Joint Method of Agreement and Difference, or 
Indirect Method of Difference), the Method of Residues, and 
the Method of Concomitant Variations. We shall give an 
account of each of them, beginning with the Method of Dif- 
ference. 

If a baby strikes or pushes a hanging ball and the ball 
moves, and if the experience happens to be repeated several 

times, the babv 2:ets in the way after a while of ex- 
The Method .' , ' ° ^ ^ 1 n 1 r , 

of Differ- pectmg that each new stroke or push will be fol- 

lowed by a new movement of the ball, and years 
afterwards it learns to say that the stroke of the hand caused 
the movement of the ball. If a man were to try the same 
experiment as the child he would reach the same conclusion, 
but, unlike the child, he might try to explain why the con- 
clusion was reasonable. If he did, his reasoning would be 
something like this : ^ Before I touched the ball it was mo- 
tionless. I struck it a great many times. Every time I 
struck it it moved. When I left it alone it gradually stopped 
moving. If my blows did not move it, what did ? I was 

^ It is hardly necessary to say that inductive inquiry existed long 
before the theories of these writers, and even a very clear theoretical 
conception of the principles on which it is founded. Minto's ''Logic" 
(pp. 243-272) gives a good account of the whole matter, including the 
views and influence of Francis Bacon and of Roger Bacon (12 14-1292), 
whom Minto calls his greater namesake. Minto, however, does not men- 
tion Hume and his remarkably clear statement of the canons for the 
methods of Agreement, Difference, and Concomitant Variations (See 
the ' Rules by which to judge of causes and effects ' in the '' Treatise of 
Human Nature "). 



THE METHOD OE DH^l^^ERENCE. 263 

alone in the room ; the liouse was quiet ; there were no sud- 
den draughts of air. It may be that a ball might be moved 
before my eyes by some cause that I could not see and do 
not know about ; but if there was any such cause, why did it 
always wait to move the ball until I struck it ? ' 

The force of this argument lies in the question ' If I did 
not, what did ? ' The man assumes that the event must have 
been caused, and the harder he looks without finding any- 
thing that might have caused it except his own activity the 
surer he feels that that was the real cause ; and if he knew 
for certain that his blow was the only change introduced 
into the situation before the ball began to move — the only 
point of difference except the movement itself between the 
situation in which the ball did not move and that in which it 
did — then he could be absolutely certain that it was his blow 
that caused the movement of the ball. It is clear enough 
that this reasoning is based on our principle of exclusion (one 
of the forms taken by the wider principle of exhaustion, see 
p. 225) ; and the italicized words explain why Mill calls 
this special application of the principle the Method of Dif- 
ference. 

It makes no difference in the method whether it is used to 
explain an actual change in one situation or the difference 
between two. If there are two precisely similar balls sus- 
pended in precisely similar manners, except that one is 
exposed to a steady wind and moving while the other is 
sheltered and stationary, we can conclude that the wind is 
the only possible cause of the movement, since it is the only 
circumstance (except the movement itself) present in one 
case and not in the other and we cannot suppose that a cir- 
cumstance present in both cases would move one ball which 
happens to be here and not move another precisely like it 
which happens to be there. 

The principle of exclusion as used in this method of dif- 
ference can be stated in the following abstract canon of 
Mill's: '' If a7i instance in which the phenomenon tmder in- 



264 THE METHODS OF DIFFERENCE AND AGREEMENT. 

vestigaiion occurs^ and an instance in which it does ?iot occur, 
have every [other'] circumstance in common save one, that one 
occurring only in the former ; the circumstance in which alone 
the two instances differ, is the effect, or the cause, or an indis- 
pensable part of the cause, of the phenomenon.'' To put the 
same thing more symbolically : If there is a case in which 
all the antecedents can be represented by the letters A, B, C, 
and D and all the consequents by the letters W, X, Y, and 
Z, and another case in which all the antecedents can be 
represented by the letters A, B, and C, and all the conse- 
quents by W, X, and Y, then the antecedent D is the cause 
or part of the cause of the consequent Z. 

A girl dressed in a blue gown and carrying some books 
walks quietly across a room and as she passes over a certain 
place a squeaky noise is heard. Soon after, a 
of Agree- boy dressed wholly differently, talking, and car- 
rying nothing at all, walks over the same place, 
and as he does so the noise is heard again. Now if we 
assume that the noise has the same cause in both cases and if 
we can be sure that walking over the same spot was the only 
circumstance except the noise that was the same in both, 
i.e., the only one in which the two instances agreed, then we 
cannot help concluding that walking over that spot caused 
the noise. The italicized words explain why this inference 
is drawn by the Method of Agreement. 

This method, like the last, depends on the principle of ex- 
clusion; for we cannot be sure that the circumstance we have 
picked out is the only point of agreement until we have ex- 
amined every other circumstance and found that no one of 
them is the same in both cases. 

In the example just given the effect was produced at the 
time of the observation, so that the things involved underwent 
a change. But the method of agreement is also applicable to 
cases in which we cannot observe the origin of the effect. 
Suppose, for example, that on the top of every high mountain 



DOES EITHER METHOD REALLY EXHAUST? 265 

which we climb we find the air to be cooler than in the sur- 
rounding country, no matter where the mountains are, what 
their shape, or what they are made of. As soon as we can be 
sure that the elevation is the only point of agreement between 
them all (except the lower temperature) we can infer that the 
greater elevation has something to do with the lower temper- 
ature. 

Mill's canon for the method of agreement is this: ''If 
two or more instances of the phenomenoii under investigation have 
only one circu??istance in common [and if that phenomenon is 
always produced by the same circumstance ; then] the circum- 
stance in which alone all the instarwes agree is the cause [or 
effect) of the given phe^iomenony To put it more symboli- 
cally : If all the antecedents in one case can be represented 
by the letters ABCD and all the consequents by WXYZ, 
and in another case all the antecedents can be represented 
byEFGD and all the consequents by KLMZ, and if Z always 
has the same cause, then D is the cause of Z. 

The methods of agreement and difference both depend 
upon the principle of exclusion, and in both methods this 
principle has been properly applied only if we Does either 
have been correct in assuming that no point of J^aliy^ex- 
agreement or difference (as the case may be) es- ^^^^^ ^ 
caped our observation. But this is no small assumption. How 
do we know that the mountains we visit do not happen by the 
merest chance to lie over relatively cool places in the centre of 
the earth, or to be packed with ice, or to lie in places where 
cool currents of air turn downwards towards the earth? How 
do we know that when the girl and the boy both passed the 
same spot a cat in the cellar did not happen to catch a* mouse 
which made the noise as it was caught ? EIow do we know 
that the ball the child struck was not possessed by a demon 
which happened to move it at that instant, and that the one 
swinging in the wind was not similarly possessed ? In short, 
it is only an infinitesimal part of nature that we can pretend 
to have observed, and how can we possibly prove that the 



266 THE METHODS OF DIFFERENCE AND AGREEIVIENT. 

only point of agreement or the only point of difference we 
happen to have noticed is the only one there is ? 

We can not ; and for that reason our inductive argument 
will always be at least theoretically inconclusive. But all 
reasoning, even deductive, is for the sake of practice ; and 
from the practical standpoint the force of this objection can 
be considerably weakened. As mere theorists the thought of 
the almost infinite search that niust be made before w^e can say 
we have found the only point of agreement or the only point 
of difference between two situations appals us. As practical 
beings it does not ; for when we begin to reason about the 
connections in Nature we are not in the position of strangers 
dropped from another universe. We are in the midst, of 
affairs. We have learned in a practical way that a vast num- 
ber of agreements and differences between situations can be 
thrown out immediately as immaterial ; and we dismiss them 
so unhesitatingly that we are inclined to laugh at the theorist 
instead of answering him when he asks how we know that the 
ball did not swing because a Chinaman laughed on the other 
side of the globe, or that the mountains we saw were not cool 
because people lived in the valleys. Thus the practical man 
approaches his inductive problem with vastly more data than 
he states ; he does not hesitate to distinguish between kinds 
of agreement and difference that may be material and those 
that are certainly immaterial ; and thus most of the elimina- 
tion is already performed. 

Not only have we this practical belief that the possible 
causes are after all not so very numerous, but we have it in our 
power to diminish the chance that any of them have been over- 
looked" by observing as many and as different cases as possible. 

The more mountains we examine and the more differenc 
there seems to be between them in every respect except 
height and coolness, the greater is the chance that there is no 
other point of resemblance common to them all. The more 
often we notice that light things begin to move when the 
wind begins to blow, the less chance there is that, in every 



ADVANTAGES OF EACH. 267 

case we noticed, some entirely different event (which we did 
not notice but which might have caused the movement) took 
place at the very instant the wind rose. Mere coincidences — 
whether in space or in time — may be expected occasionally, 
but occasionally only. 

Whether we shall use the Method of Difference or the 
Method of Agreement in any particular case often depends 
upon what data we have to work with; and Advantages 
therefore we cannot always choose between them. °^ ^^^^' 
It is worth while nevertheless to discuss some of their relative 
advantages and disadvantages. 

The methods of Difference and Agreement are both subject 
to the defect already pointed out that we may fail to observe 
or consider some essential circumstance, and may thus mis- 
take some merely accidental concomitant for the true cause. 
With the method of Difference the circumstance overlooked 
would be a point of difference between the objects com- 
pared ; with the method of Agreement it would be a point 
of agreement. 

A much more certain and important difference in the 

practical application of the two methods grows out of the 

fact that much the same result can often be pro- 
j J 1 r 1 ^r Plurality of 

duced by any one 01 several causes. You can possible 

causes, 
kill a man in a great many different ways ; you 

can poison him with any one of a great many different drugs. 
Rain is not the only thing that can wet a lawn ; and sunshine 
is not the only thing that can dry it. "This is called the princi- 
ple of the Plu7'alUy of Possible Causes or the Vicariousness of 
Causes, Let us see how it affects each of our methods. 

If we find the antecedents ABC accompanied by the con- 
sequents XYZ, and the antecedents AB accompanied by the 
consequents XY, and if we know that these are all the essen- 
tial facts, we can conclude that, under the circumstances 
AB, C is the cause or a necessary part of the cause of Z. 
This is the method of difference, and it is not affected by the 
plurality of possible causes. 



268 THE METHODS OF DIFFERENCE AND AGREEMENT. 

But suppose that in one case we have the antecedents ABC 
and the consequents XYZ, and in another the antecedents 
EFC and the consequents VWZ, and that these are all the 
essential circumstances. If Z has the same cause in both 
cases, we know that it cannot be anything but C ; but it need 
not have the same cause in both cases. How do we know, 
then, that it is not caused by A in one case and by E in the 
other? If I have coffee, toast, and eggs for breakfast one 
day, and water, hot biscuit, and eggs the next, and if I have 
indigestion on both days and know or assume that in each 
case it v/as caused by something which I had for breakfast, 
it may have been caused by the eggs on both occasions ; 
and in the absence of any further information that is the 
most natural inference. And yet it is possible that the 
trouble was due to the coffee on the first day and to the hot 
biscuit on the second, while the eggs were all the time per- 
fectly harmless. 

This plurality of possible causes constitutes what Mill calls 
^' the characteristic imperfection''' of the Method of Agree- 
ment, — an imperfection which makes it distinctly inferior to 
the Method of Difference. 

Where answers suggested by the method of agreement 
cannot be tested by some form of the method of difference, 
the uncertainty arising from the plurality of possible causes 
can be indefinitely diminished by the multiplication of vari- 
ations. If we cannot try the eggs alone, it may be that we 
can try them with different accompaniments on a great many 
different days, until we are driven to the conclusion that if 
they do not cause the trouble, they are about the only things 
one can eat that do not. But farther than this we cannot 
go by the Method of Agreement ; and it is not often we can 
go so far. 

This difficulty growing out of the plurality of possible 
causes I have spoken of as practical. It is due partly to the 
practical impossibility of ascertaining all the antecedents and 
all the consequents in any set of cases, partly to the practical 



PLURALITY OF POSSIBLE CAUSES. 269 

impossibility of distinguishing with absolute accuracy or cer- 
tainty between relevant and irrelevant circumstances, and 
partly to our careless way of ignoring the distinction between 
different conditions so long as they are called by the same 
name. So long as we know merely that ^ we have indiges- 
tion after breakfast ' in all the cases mentioned, we cannot 
tell whether it was caused by the same thing every time or 
by different things ; but if we took the trouble to find out 
each day how soon after the meal the attack arose, precisely 
how severe it was, how long it lasted, and every other ob- 
servable detail, we should soon be able to say whether the 
trouble really was the same in all the cases, as our first, rough 
statement implied, or in fact quite different. If it was pre- 
cisely the same in every relevant respect, we could be quite 
sure that in each case the attack was caused by the same 
thing — namely, the eggs ; but if we found constant variations 
in the symptoms, and if we could be sure (as we cannot) 
that variations in the things eaten for breakfast, as distin- 
guished from previous conditions or the manner of eating, 
were the only possible cause of these variations, and that the 
eggs eaten were all precisely alike in every essential respect, 
then we could be quite certain that the eggs were not the 
cause, or at least not the only cause, of the symptoms. 

Theoretically I think we must admit that no two causes in 
the world could be substituted for each other and leave pre- 
cisely the same results everywhere ; and therefore to a perfect 
intelligence dealing with perfect data there would be no such 
thing as a plurality of possible causes. I think we must 
admit, too, that in many cases where we seem to be confronted 
by such a plurality of possible causes the difficulty is due to 
careless and avoidable inaccuracy ; but, on the other hand, I 
think it cannot be doubted that in most cases the difficulty is 
due to the fact that in this practical world we learn a great 
many things vaguely before we learn anything accurately ; so 
that when any particular question, such as the cause of indi- 
gestion, arises we cannot expect anybody to know everything 



270 THE METHODS OF DIFFERENCE AND AGREEMENT. 

else SO well that he can distinguish the relevant antecedents 
and consequents from the irrelevant. In a purely hypo- 
thetical case a person might be supposed to know that his 
indigestion after breakfast had absolutely nothing to do with 
the supper he ate the evening before, or with the soundness 
of his sleep during the night, or with what he read in the 
morning newspaper, and so on ; and yet not to know what 
really did cause it. But in most actual cases the facts are 
reversed and we have to know what caused the trouble before 
we can find out what circumstances were irrelevant — we can- 
not state our problem with refinement until we have solved 
it. And so ^ the characteristic imperfection ' of the method 
of agreement remains. We can only say that the more we 
know to begin with and the more carefully we distinguish 
slight differences, the less trouble it will give. 

Let us now compare inferences — whether drawn by the 
method of difference or by that of agreement — which are 
Two kinds based upon the comparison of two changeless sit- 
pared. " nations with those which are based upon the ob- 
servation of changes taking place in one. 

One advantage in having a changing situation when we 
are seeking for causal relations is that it sometimes enables us, 
though not always, to distinguish between causes and effects. 
If we find one place where the soil is moist and vegetation 
luxurious, and another where moisture and vegetation are 
both absent, we cannot say whether the moisture causes the 
vegetation or the vegetation the moisture; but when we 
notice things begin to grow after a rain we can be quite sure 
that in this case at least the growth of the vegetation is not 
the cause and the moisture the effect. If either of them is 
the cause of the other, it is the moisture. In comparing two 
changeless situations we talk of antecedents and consequents 
just as we do in speaking of changes ; but here the words 
are used rather metaphorically, ^ antecedent ' meaning one of 
a group of causes, and ' consequent ' one of a group of 
effects ; and we cannot tell which of two circumstances 



TWO KINDS OF DATA COMPARED. 271 

should be called the ^antecedent' and which tlie ^conse- 
quent ' until we have found out in some indirect way which 
of the two is cause and which effect. Where there is a change 
we can often see directly which event is antecedent, and 
therefore cause, and which is consequent, and therefore effect. 
Yet this advantage in reasoning from a changing situation 
is rather dubious, so long at least as we are mere observers. 
Often we notice a situation changing without being able to 
tell which element in it changes first. We feel the breeze 
arising and see the aspen leaves begin to quiver or the trees 
begin to sway. But do we really observe which came first ? 
Can we prove by direct observation alone that the breeze 
really came first and was therefore the cause — and not the 
effect, as children sometimes suppose — of the fan-like swaying 
of the trees ? It is only when there are a number of inter- 
mediate links in the chain that the interval in time between 
causes and effects is really perceptible. Then, again, the 
observation of the apparent order in time often positively leads 
us astray. Is the sound of thunder caused by the flash of light 
because we hear it afterwards ? Does the falling of the ba- 
rometer cause rain because it precedes it ? The fact is that 
observation of the order in time does not help us to tell which 
of two events is the cause and which is the effect nearly so much 
as does a knowledge of other causal relations. We do not 
believe that the wind moves the trees, and not the trees the 
wind, because we see that the wind comes first, but rather 
because we do not know anything but wind that is likely to 
move the trees, while we do know something besides the trees 
that can stir up the wind. One theory leaves a broken 
causal chain and the other does not. In other words, a state 
of affairs in which the wind moves the trees fits into the rest 
of the world as we know it better than one in which the 
movement of the trees causes the wind; and so we assume 
that the former state of affairs and not the latter is the real 
one. But such reasoning as this is quite as applicable to 
cases in which there is not any change as to those in which 



2 72 THE METHODS OF DIFFERENCE AND AGREEMENT. 

there is. Thus this advantage which reasoning about change 
seems to possess over reasoning about situations which do not 
change is often only apparent. 

When we assume that one event must be the effect of an- 
other merely because it follows it — 'post hoc ergo propter hoc ' 
— we commit a very common blunder, which 
ergo propter is sometimes called the fallacy of ' False Cause ' , 
^^* but is more commonly designated by the Latin 

phrase which describes the reasoning. 

Whether the cases compared compel us to draw our infer- 
ences by the method of agreement or by the method of dif- 
ference, and whether we are comparing two dif- 
Advantagfes r . . .- i i 

of expert- ferent situations or the changes m one, are not 

nearly so important questions as one not yet men- 
tioned. This is the question whether we merely observe and 
compare situations as we happen to find them or whether we 
deliberately create them for the purpose of answering specific 
questions : the question whether our inference is based upon 
mere ' observation ' or upon ' experiment '. 

Mere observation often raises problems ; but when they 
are once raised, experiment, where it can be tried properly, 
gives the more satisfactory answers. 

In the first place, the very object of experiment is to pro- 
duce conditions which are thoroughly understood and from 
which all disturbing factors are, so far as possible, removed. 
Hence when we experiment there is much less chance that 
some real cause has been overlooked than when we merely 
observe some of the occurrences that take place amidst the 
great confusion of natural conditions. 

A second point in favor of experiment is that it enables us 
to tell, as observation does not, not merely that a pair of cir- 
cumstances have some direct or indirect causal relation, but 
that one is the actual cause of the other, and which one that is. 

We have just seen (p. 271) how these questions can often 
be settled indirectly, through our knowledge of the rest of the 
world. Experiment often enables us to settle them directly. 



ASSUMPTION IN EXPERIMENT. 273 

If I blow air against the branches of a tree, they will begin 
to move; and from this I conclude that in this case at least 
the movement of the air is the cause and the movement of the 
tree the effect. On the other hand, if I sway a tree, a little 
breeze will arise ; and from this I conclude that in this case 
the movement of the tree is the cause, and the movement of 
the air the effect. So I say that either may cause the other. 
Again, if I heat the air around a thermometer, I will find the 
mercury rise ; but if I raise the mercury in some other way, I 
will not find any noticeable change in the temperature of the 
surrounding air ; so I conclude that the temperature affects the 
height of the mercury, but not vice versa. Still again, if I 
forcibly lower the mercury in a barometer, a storm will not 
follow; and if I make a little rainstorm around it with a 
watering-pot without lowering its temperature, the mercury- 
will not fall. So I conclude that the fall of the mercury does 
not cause the rain, or the rain the fall of the mercury, but 
that when the two are found together they must be joint 
effects of the same cause ; and if I guess what that cause is, I 
may be able to verify my guess by a new set of experiments 
designed to test the relative weights of air and watery vapor, 
and the effect produced upon the mercury in a barometer by 
the pressure of such different weights. 

We can reach all these conclusions by experiment because 
we take for granted the relative spontaneity of our own vol- 
untary acts. It may be that we ourselves are as 

, - 1 . 1 ^ ^ Assumption 

much a part 01 nature as anything else and that inexperi- 

every one of our acts is the necessary effect of 
some preceding cause. But we assume that we know enough 
about ourselves to be sure that the immediate causes of our 
acts are very different from the immediate causes of such 
things as wind, temperature, and rain. If we did not make 
this assumption, we should have to assume that our own acts 
in various experiments and the results which seem to follow 
from them might be merely joint effects of the same causes. 
Hence we could not be sure that our blowing of the air made 



I 



274 THE METHODS OF DIFFERENCE AND AGREEMENT. 

the tree move, or that our squeezing of the bulb or our heating 
of the air around it raised the mercury in the thermometer. 
For unless we assume our own relative independence it might 
well be that there was some general state of affairs which made 
the tree sway and at the same time made our brain-cells dis- 
charge and our muscles contract as though we were swaying 
it ; and so with the other examples. On the other hand, if 
our voluntary acts are spontaneous so far as the events which 
we are investigating are concerned, — if they are never mere 
effects of preceding events in the series under consideration,— 
then, though these voluntary acts and the changes around us 
which follow them may sometimes coincide through mere 
chance, they can never be joint effects. If there is any 
causal relation between them at all, the voluntary acts must 
be the causes, and the changes that follow must be their 
effects.^ 

* A third advantage connected with experiment is that inferences 
based upon it are accompanied with a greater feeling of satisfaction. 
The feeling of muscular exertion which comes with our own acts is as- 
sociated very closely in the minds of most people with the idea of cause 
and effect or is really a part of it. Consequently the actual production 
of an effect by our own exertion seems to give an immediate feeling of 
the causal connection that nothing else can give. 



CHAPTER XXVII. 
THE JOINT METHOD OF AGREEMENT AND DIFFERENCE. 

For a perfect application of the Method of Difference, as 

we have seen, there must be two cases ahke in every respect 

except that in one a certain effect and its cause 

/ , , - P ,. . ^ Its function. 

are both present ; and for a perfect apphcation of 

the Method of Agreement there must be two cases different 
in every respect except that the causally related circum- 
stances are present (or, it might be, absent) in both. More- 
over there is always danger that the method ♦in question has 
not been applied perfectly, because of the possible presence 
of other points of difference or resemblance which .have not 
been noticed. But suppose that other points of difference or 
resemblance are present and are noticed, and that we cannot 
find any two cases in which they are not ; is inference no 
longer possible ? 

It is not possible if there are only two such cases ; but if 
there are more and they differ widely from each other, it may 
be. Suppose, for example, that we have all the following 
combinations, the letters from A to M standing for known 
antecedents, the letters from N to Z for known consequents, 
and the blanks for other possible but unknown antecedents 
and consequents. 

i) ABCDEF-NOPQRS- 4) BCDE-OPQR- 

2) ABGHI-NOTUV- 5) CFGH-PSTU- 

3) ACGKL-NPTXY- 6) EHIJKL-RUVWXY- 

275 



276 JOINT METHOD OF AGREEMENT AND DIFFERENCE. 

We notice that where A is present N is present, and that 
where A is absent N is absent (which is the same thing as 
saying that where A is present N is present, and where N is 
present A is present); and this suggests that A is the cause 
of N. But how shall we prove it ? The Method of Differ- 
ence is inapplicable, because there are no two cases (not 
even the first and the fourth) that differ in no respect except 
the presence of A and N in one case and their absence in the 
other. In the same way there are no two cases from which 
we can prove the connection by the Method of Agreement. 

Yet there is a way in which the Method of Agreement can 
be applied, and applied doubly. Assunwig that the cause of 
N is to he fou7id amongst the observed antecedents and that it 
is always the same, we can prove from the first two cases 
that it is either A or B or the combination AB, for A and B 
are the only conditions present in both. From the first and 
third cases we can prove in the same way that the cause is 
either A or C or AC ; and from the second and third that 
it is either A or G or AG. And if, as we have assumed, the 
cause is the same in all the cases, it must be A. Thus, though 
the presence of A and N is not the only respect in which any 
two cases agree, it is the only known respect in which all the 
three positive cases agree, and A is therefore the cause of N, if 
the cause of N is always the same observed circumstance. 
This IS a perfectly legitimate application of the Method of 
Agreement; but, like all applications of that method, it is 
subject to the objections that the cause of N may not be the 
same in all cases, and then even if it is, the real cause may 
be some unknown circumstance, represented by one of the 
blanks. 

The Method of Agreement can be applied, again, to the 
negative cases 4, 5, and 6. These all agree in the absence 
of A and N, and if instead of only three relatively simple 
cases we had a great number that were quite complex (as we 
often have in Nature), we might be inclined to say that the 
absence of A and N was the only respect, or rather the only 



ITS FUNCTION. 577 

respect worth considering, in which all these cases do agree. 
In this way we might have a double assurance, one from the 
positive cases and one from the negative, that A was the cause* 
of N. The negative cases have this advantage : inference 
based upon them is not subject to the objection arising from 
the plurality of possible causes. If the absence of A is always 
accompanied by the absence of N whether any other ante- 
cedent is absent or not, then A not only may be the cause of 
N, but must be ; and it must also be the only possible cause. 
On the other hand the negative cases are subject to the tre- 
mendous disadvantage that it is practically impossible to 
prove a negative, to show that a pair of given circumstances 
are the only ones which can not be found in any of the cases. 
Consequently, when negative cases are taken by themselves' 
they are much more dangerous to work with than positive. 
Yet so far as they go they tend to confirm the results based 
upon the positive cases, and they suggest at least that in all 
the cases observed there was only one cause. Because results 
based upon negative instances of this sort can be regarded 
as confirming those based on the positive, the employment 
of the two is called by Fowler * the Double Method of 
Agreement. 

But these positive and negative instances can be looked at 
from another standpoint, and regarded as data for an indirect 
application of the method of difference. We can say: ^ When 
N is present and every condition but A can be varied without 
causing its disappearance, these conditions are necessarily 
immaterial. In the same way when every condition but the 
absence of A can be varied without causing its appearance, 
these conditions also are immaterial. But the distinction be- 
tween immaterial conditions may be ignored ; therefore the 
only important distinction between the two sets of cases is that 
in the one A and N are both present, and in the other they 
are both absent. ' And this is all we need for the method of 

* " Inductive Logic ", Macmillan, 1889. 



278 JOINT METHOD OF AGREEMENT AND DIFFERENCE. 

difference. Hence the double method is called by Mill the 
Indirect Method of Difference. Because the method of agree- 
ment and the method of difference are both involved it is also 
called by him the Joint Method of Agreement and Difference. 

Mill's canon for the method is this : 

''^ If two or more instances in ivhich the phenomenon occurs 
have only one circumstance in co?7i?non, while two or more in- 
stances in which it does not occur have itothing in co77imon save 
the absence of that circu?nsiance, the circumstance in which 
alone the two sets of instances differ is the effect^ or the cause, 
or an indispensable part of the cause , of the phe^iomenon^ 

''This method", Mill says, ^'may be called the Indirect 
Method of Difference, or the Joint Method of Agreement 
Compared ^^d Difference; and consists in a double employ- 
metko^d^f*^^ ment of the Method of Agreement, each proof 
difference. being independent of the other and corroborat- 
ing it. But it is not equivalent to a proof by the direct 
Method of Difference. For the requisitions of the Method 
of Difference are not satisfied unless we can be quite sure 
either that the instances affirmative of a [i.e., N, the con- 
sequent in question] agree in no antecedent whatever but 
A [the antecedent in question], or that the instances nega- 
tive of a agree in nothing but the negation of A. Now, 
if it were possible, which it never is, to have this assurance, 
we should not need the joint method ; for either of the two 
sets of instances separately would then be sufficient to prove 
causation. This indirect method, therefore, can only be re- 
garded as a great extension and improvement of the Method 
of Agreement, but not as participating in the more cogent 
nature of the Method of Difference. " * 

Mill is right in saying that the Joint Method will not give 
absolute certainty. But then neither will the Method of Dif- 
ference, applied in our common human ignorance of a vast 
number of surrounding conditions. A theoretically perfect 

* <^ Logic", Bk. Ill, Chap. VIII, Sec. 4. 



COMPARED WITH SIMPLE METHOD OF DIFFERENCE. 279 

application of the Method of Difference will give a theoret- 
ically perfect proof; but none of our applications of the 
method are theoretically perfect, and a good many of them 
are not practically perfect either. Mill and other writers on 
logic tell us that experiments are usually based upon the 
Method of Difference and that that is one reason why experi- 
ment is better than mere observation. It is true that they are 
based on that method in any single experiment, — we add one 
new circumstance and see if the effect in question follows. 
But why are the conclusions based on experiment sometimes 
erroneous ? Why do scientists all over the world try to re- 
peat and thus Werify ' each others' experiments, if any one 
could be sure that the method was rigorously applied the first 
time ? The fact of the matter is that in all cases where 
experiment is possible, whether in common life or in science, 
the final appeal is not usually to the Method of Difference, 
but to the Joint Method. I destroy a frog's brain, suspend 
the creature by the nose, and dip its foot into a solution of 
acid ; and a second or two later I see the foot lifted out of 
the acid just as if the brainless frog knew what it was doing. 
By the Method of Difference I reason that the contact with 
the acid was what made the frog lift the foot up. But am I 
satisfied with this one experiment ? If such an occurrence 
happens to be unfamiliar and I am really interested in the 
question, will I not try the experiment again under as many 
different conditions as I can think of, and ask others to do the 
same? And if everybody gets the same result, will they not 
then have two groups of cases to compare, the members of 
each group varying in as many respects as possible except the 
two in question ? In one group there are all the cases in 
which the foot has not yet touched the acid and has not been 
drawn up; in the other are all the cases in which the foot has 
touched the acid and has been drawn up. And these are the 
kind of data to which we apply the Joint Method. 

In conditions known to be theoretically perfect one 
experiment based on the Method of Difference would be 



2 8o JOINT METHOD OF AGREEMENT AND DIFFERENCE. 

sufficient to give absolute proof of a causal relation; but 
because there are always a great many possible sources of 
error, we can always feel surer of conclusions when the 
experiments upon which they are based have been performed 
many times under different conditions than when they have 
been performed only once. And thus even where the 
Method of Difference is most applicable we appeal from it 
to the Joint Method. 



CHAPTER XXVIII. 

COUNTERACTING AND COMPLEX CAUSES. 

We have reasoned thus far on the assumption that an 
adequate cause is invariably accompanied by its effect. 
We have virtually said : * The effect may be present with- 
out this particular cause, because the same effect counteract- 
may be due to any one of several causes; but ^^8^ causes, 
that does not imply that the cause can be present without 
its effect, and if what we supposed to be a cause of a given 
effect is ever found to be present without the effect, we were 
mistaken in supposing it was the cause (though it might have 
been part of the cause). If A causes N, N may sometimes 
be present without A, but A can never be present without N. ' 
This is the principle on which we have been reasoning up 
to the present, and if we were in a world in which nothing 
else could ' come between ' A and N, or affect their relations 
to each other, reasoning based on this principle would 
always be correct. As it is, it is not. It may be that A is 
a perfectly adequate cause of N and yet that it is sometimes 
present without N. In the presence of a ' Counteracting 
Cause ' a cause perfectly adequate in itself will fail of its 
effect. The swift current of a river causes things floating in 
it to drift down the stream; and yet if there is a hurricane 
blowing in the opposite direction, the things may drift up 
and not down. The working of the engines makes the ship 
move; but now she is fast on the rocks and for all their 
work the engines cannot move her. 

281 



282 COUNTERACTING AND COMPLEX CAUSES. 

Without going into any theoretical discussion, the prac- 
tical lesson to draw from such cases is this : There is a differ- 
ence between saying that a cause always produces its natural 
effects and saying that it always tends to produce them; and 
this latter is all we have a right to say. Put more concretely, 
this rule means that if we are searching for the cause of a 
given effect N and find that A is sometimes present when N 
is not, we must not conclude from this that A is not the 
cause of N, until we are sure that there is nothing present 
which can counteract A's effect. 

If we know what can counteract the effect of A, or, what 
amounts in this case to the same thing, what can prevent 
the production of N, our task of discovering the relation 
between A and N w411 be easy enough. But if we do not 
know enough about either A or N to say what would prevent 
the one from causing the other, then our task will be very 
much more difficult. If A and N occur together often 
enough to make us suspect that A is really a cause of N, 
though sometimes counteracted in its working by G, H, or 
J, we must simply leave the matter doubtful until we can 
make or find conditions simple enough or varied enough to 
let us infer something about the real nature of some of these 
influences. 

Sometimes a situation may be so complicated that we have 
to deal not only with several kinds of causes and counter- 
acting causes, but with still other antecedents that counteract 
the counteracting causes. But however complicated our 
problem may be, the principle of exclusion upon which we 
must depend for its solution remains the same. 

The possibility of counteracting causes makes it possible 
to commit a blunder of precisely the opposite kind from that 
made possible by the plurality of possible causes. If we 
forget that practically the same effect can be produced by 
any one of several causes, w^e may assert that something is 
the cause of this effect, when it is not the cause at all, simply 
because it happens to be the only one thing present in all 



CAUSES 'COMPOUNDED' OR 'COMBINED.' 283 

the cases we have observed. On the other hand, if we forget 
that a cause is sometimes counteracted, we may deny that 
something is the cause, when it really is, because it is some- 
times present without the effect. Thus, if we are careless, 
the presence of a plurality of causes may make us find false 
causes, and the presence of a counteracting cause may make 
us overlook true ones. 

Methods of investigating causal relations have been dis- 
cussed thus far as though we assumed that every effect had 
some one simple cause and every cause some one 
simple effect. But it often happens that several pounded* or 
causes act together to produce a given effect and 
that there is some reason why we should not regard them as 
one. 

There are two ways in which causes can act together 
to produce a joint efiect. Sometimes the effect of each one 
of them separately is like that of each of the others and like 
that of the group as a whole. Sometimes the separate effect 
of each is unlike the effect of each of the others, and the 
effect of all together is unlike the effect of any one. Here 
is a case of the first sort. The amount of money that a man 
has at the end of the year depends upon how much he had 
to start with, what he made or lost each day in his regular 
business, what he made or lost in other ways, what he spent 
for regular household purposes, what he spent for amuse- 
ment, what he gave away. In his cash account he sets down 
all the expenditures on one page and all the receipts on 
another, adds all the items on the same page together, and 
subtracts them from the total of the other page. In his 
balance it makes absolutely no difference what the money 
that he spent w^as spent for. If he wants a certain balance 
and finds before the end of the year that he is spending too 
much for rent and groceries, he may make up for it by 
cutting down his expenditures for recreation and charity. 
All the forces dealt with in mechanics are causes of this sort. 
When one is ' added to ' or ' subtracted from ' another the 



284 COUNTERACTING AND COMPLEX CAUSES. 

result is precisely the same as it would have been if the body 
on which they are acting had been acted upon by only one 
force equal to the sum or the difference. In mechanics we 
speak of the ' Composition of Forces ' ; and Mill paraphrases 
the term and speaks of the ' Composition of Causes ' when 
the effect of them all can be considered in this way as the 
algebraic sum of the effects of each of them. The separate 
causes and effects which are thus added together he speaks 
of as ' Compounded '. 

Now for the second kind of joint effects. To raise a crop 
of onions there must be seeds, air, moisture, w^armth, and 
soil. If any one of these is left out, the result is, not smaller 
onions or fewer onions, but no onions at all. Moreoyer if 
a farmer finds that his onions are getting too much heat from 
the sun, he cannot even things up by giving them so much 
less water. In the same w ay if a cook finds that she has put 
too much sugar into her cake, she cannot improve matters 
by leaving out the flour. Cooking is a matter of chemistry, 
and chemistry is full of examples of this kind of joint effects. 
Oxygen and hydrogen ' combine ' to form w^ater, whose 
appearance and action are quite different in almost every 
respect from those of either of them. In the same way the 
green poisonous gas chlorine ' combines ' with the very 
different yellowish metal sodium to form common salt, wdiich 
again is very different from either of them. Joint effects 
v/hich differ in this way from the effects of any of the causes 
separately are called ' Heteropathic ', and since the effect 
of uniting the causes is like that of making a chemical 
' combination ' the causes are said to be ' Combined \ 

To produce heteropathic or combined effects it is neces- 
sary that the causes concerned should all be present at the 
same time or follow each other in some fixed order. If the 
onion seed is to grow, it must be warmed and moistened after 
it is put in the soil, not before; if the cake is to taste right, 
its various ingredients must be mixed before it is cooked, 
not afterwards, To produce compound effects this is not 



CAUSES ^COMPOUNDED' OR ^COMBINED.' 285 

necessary. The onions weigh as much whether they are all 
thrown into the basket at once or one after the other; the 
ingredients of the cake cost as much whether they are all 
purchased at the same time or at different times. The 
* parallelogram of forces ' in physics is a graphic way of 
explaining that when a body that can move freely is acted 
upon by several forces at once it reaches the same point 
(though it travels along a diagonal) as it would have reached 
if it had been acted upon by the same forces one after the 
other. 

Because mathematics can be applied freely in calculating 
the joint effect when causes are ' compounded ' but cannot 
be so applied when they are ' combined ', we have made a 
distinct advance in knowledge w^hen we can say beforehand 
in which way they will be conjoined. For example, it is a 
great advantage if we can be sure that the weight of a com- 
pound, however formed, is always equal to the compounded 
weight — i.e., to the sum of the weights — of its ingredients. 
According to an old story the Royal Society w^as once tricked 
into discussing the question why it was that nothing is added 
to the weight of a vessel of water when a live fish is put into 
it; and the discussion of one explanation after another went 
on for a long time before any one suggested that they try the 
experiment and see whether what they were trying to explain 
was really the case. The moral naturally attached to the 
story is that it is wise to find out whether a fact exists before 
you try to explain it; but here it is used to illustrate some- 
thing else. If any one were quite sure that the weight of 
any body is a compound effect made up of the weight of all 
its separate parts, he would not think it necessary to try the 
experiment at all. He could be sure beforehand that an 
addition of any kind to the contents of the vessel w^ould 
increase its weight, and he would know^ that whether the fish 
put into it were alive or dead could make no possible differ- 
ence. If the Royal Society ever did seriously discuss such 
a question as this, it must have been when physicists weiQ 



286 COUNTERACTING AND COMPLEX CAUSES. 

not all certain that weight is a compound effect and never 
under any circumstances or to any extent heteropathic. 

The distinction between 'compounded ' and 'combined ' 
causes can be applied quite as well when some of the causes 
tend to counteract the effects of the others as when they all 
assist each other. 

A counteracting cause of the ' combined ' sort simply 
breaks up or nullifies the combination that would otherwise 
have produced the effect in question. If somebody puts 
out the chemist's fire and does it soon enough, the combina- 
tion which he expected will not occur. If a man quarrels 
with his employer and loses his place, or if the employer fails 
and cannot pay the man for his work, the quarrel or the 
failure is not a kind of expenditure that tends according to 
its amount to counteract the effect of the man's earnings. 
It puts an end to his earnings altogether. The effect of 
these counteracting causes is ' heteropathic \ 

A counteracting cause of the ' compounded ' sort simply 
adds a negative result to the positive one produced by the 
causes that it is said more or less to counteract; and conse- 
quently in calculating the net result we have merely to sub- 
tract one set of results from the other. Thus the spending 
or giving away of money tends according to its amount to 
counteract the effect of earning it, and if we wish to find the 
gain or loss during the year we have only to subtract the 
expenditures from the receipts or vice versa. Here the effects 
are not ' heteropathic \ but ' compounded \ 



CHAPTER XXTX. 

THE METHODS OF RESIDUES AND CONCOMITANT 
VARIATIONS. 

When we explain any state of affairs, such as a man's 
financial balance at the end of the year, as the ' com- 
pounded ' effect of a number of different causes, 

- , . r. IT r Quantitative 

and when we give figures to show the amount oi treatment of 

causes 

the total effect contributed by each, it is evident 
that we are dealing with the question of causation from the 
quantitative standpoint. It is no longer a mere question of 
whether a certain kind of cause was present or not, but it is 
a question also of its precise amount. If a man's actual 
balance and the balance shown by his cash account do not 
agree, there is something which has not been accounted for, 
and the causal explanation of his financial standing is not 
complete. This quantitative treatment of a question of 
cause and effect evidently rests on the assumption that the 
cause of every event must be capable of producing precisely 
that amount of effect, no more and no less. 

Because we have a right to demand an explanation for the 
precise amount of every effect as well as for its quality two 
other methods of causal inquiry can be added to the three 
already considered : the Method of Residues and the IMethod 
of Concomitant Variations. They both depend upon a 
quantitative application of the Method of Difference. 

For the Method of Residues Mill lays down the following 
canon: ''' Subtract from any phenomenon such part as is known 

287 



2 88 METHOD OF RESIDUES. 

by previous induciions to be the effect of certain .antecedents, and 
Method of ^^^^ residue of the phenomenon is the effect of the 
Residues. remaining antecedents/' If we know that a man 
has an annual income of $3200, and if we know that his 
salary is $2000 and that the annual dividend on his railroad 
stock is $500, then we can infer that he has some other 
source or sources of income that produce $700 a year. 
And if we happen to know that his only other source of 
income is his share in an iron company, we can infer still 
further that the iron company pays him a dividend of $700 
a year, no more and no less. Similarly, if a man in a posi- 
tion of trust, with a salary of $1000 a year and no private 
fortune, is spending $5000 a year, his employer will have 
reason to suspect that the man is stealing or has stolen from 
him enough to make the difference. To take still another 
illustration: Suppose we know that the planet Uranus is 
acted upon by the attraction of the sun and of the planets 
nearest to it, Jupiter and Saturn, in such a way as to bring 
it to a certain place at a certain time; and suppose that 
when the time comes the planet is not there: then we can 
be sure that if our previous calculation was correct, there is 
some other force acting on the planet and that this force is 
just strong enough to drag it from the place where the cal- 
culation showed that it ought to be to the place where it 
actually is. By calculating the strength and direction of such 
an additional force acting on Uranus the planet Neptune was 
actually looked for and discovered. 

The difference between the Method of Residues and the 
ordinary Method of Difference does not lie merely in the 
fact that the Method of Residues considers questions of 
quantity; for the next variation of the Method of Difference 
that we are about to consider does that also. It lies rather 
in the fact that when we use the Method of Difference our 
knowledge of what happens when the residual cause is not 
present is gained from direct observation, — we see what 
happens when all the causes except the one under investiga- 



METHOD OF RESIDUES. 289 

tion are present together. With the Method of Residues we 
do not directly observe what happens when all the causes 
except the one in question are present together. We only 
calculate it from what we know of the way in which they act 
when they are present separately. 

The Method of Residues is attended in practice by three 
dangers. 

The first danger is that in making our subtraction we may 
overlook the ' combined ' or heteropathic effect of some of 
the causes which we subtract, and thus attribute too much 
to the remaining causes. For example, three persons, A, B, 
and C, are in a room from which we hear the sounds of a 
violent disturbance. We know by previous inductions that 
A's disposition is quiet and peaceable; we know the same 
about B; and so we conclude that C is responsible for the 
disturbance. And yet we may be wrong, for however quiet 
and peaceable A and B may be in themselves, there may be 
something about them — some trait of disposition or some 
old misunderstanding — that makes a conflict almost inevi- 
table when the two are together. 

The second danger to which we are exposed in using this 
Metliod of Residues is that of overlooking some circumstance 
that is really present, and of thus attributing an entirely false 
value to the presence of something else. It may be that the 
man whose income we were inquiring about a little while 
ago has an allowance from his grandfather, of which he says 
nothing, and that the iron company is a source not of 
income but of expense; and it may be that the man sus- 
pected of peculation is getting an immense royalty, that his 
employer knows nothing about, from a patent. 

The third danger is that even when the data are all correct 
there may be a blunder somewhere in our calculations. If 
the bookkeeper has made a serious mistake in his addition 
or subtraction, all the reasoning by which we prove that a 
certain transaction ' mxust ' have been responsible for a gain 
or loss of such an amount is worse than useless. 



290 METHOD OF CONCOMITANT VARIATIONS. 

Of course the way to make sure that we have not been 
misled by any of these blunders is to try the residual cause 
by itself and see if it really does produce the precise effect 
indicated by the calculations. Often it does not, and where 
this is the case and the calculations are all correct it indi- 
cates that there is still another residual cause or group of 
causes to be looked for. Often, of course, direct experiment 
is impossible, and then we have to get along as best we can 
with the abstract calculations. 

In spite of its difficulties " the Method of Residues is one 
of the most important among our instruments of discovery. 
Of all the methods of investigating laws of nature, this is the 
most fertile in unexpected results: often informing us of 
sequences in which neither the cause nor the effect were 
sufficiently conspicuous to attract of themselves the attention 
of observers. The agent C [i.e., the residual cause] may be 
an obscure circumstance, not likely to have been perceived 
unless sought for, nor likely to have been sought for until 
attention had been awakened by the insufficiency of the 
obvious causes to account for the whole of the effect. And 
c [the residual effect] may be so disguised by its intermix- 
ture with a and d [the effects whose causes are already 
known] that it would scarcely have presented itself spon- 
taneously as a subject of separate study.'' * 

The Method of Residues is, like all the rest, a method of 
exhaustion; for we cannot be sure that a given residual effect 
is due, or at least partly due, to a certain residual antecedent 
until we are sure that that residual antecedent is the only 
one present that could have any influence on the effect. 

Often it is impossible to use any of the methods already 

discussed, at least without modification, simply because it 

is impossible to find or to make cases in which 
Method of ,, r 

Concomitant all of several possible causes are not present. 

Suppose that we want to know what makes a 

wheel stop turning after a while, or a pendulum stop swing- 

* Mill ; Bk. Ill, Chap. VIII, Sec. 5. 



METHOD OF CONCOMITANT VARIATIONS. 29I 

ing, or a sleigh stop sliding along a smooth and level road. 
It may be the nature of all material things to stop moving 
and come to rest, or it may be the presence of the earth that 
makes them do so, or it may be friction or some resisting 
influence exerted by the air. How are we to tell ? We 
cannot experiment for the sake of comparison with things 
that are not material; we cannot get away from the earth; 
we cannot create conditions in which there is absolutely no 
friction and absolutely no air or other surrounding medium. 
We cannot eliminate any of these possible causes. How 
then can we choose between them ? 

Though we cannot wholly eliminate any of them, we can 
introduce changes in some of them, and if we find that the 
variation of any condition is accompanied by a variation in the 
result in question, then we can be sure that that condition 
has some causal connection with the result. We know that 
the presence of the air has something to do with the move- 
ments of bodies, because we know that things stop moving 
sooner when the wind is against them than when there is no 
wind at all, and sooner when there is no wind at all than 
when it is moving with them. If the air exerted no influ- 
ence, the direction in which it moved could make no 
difference either. This proves that air exerts an influence, 
at least when it moves. That stationary air also exerts an 
influence and that this influence tends to make a thing stop 
moving can also be proved; for a pendulum will swing or a 
wheel will turn longer in a box from which the air has been 
partially exhausted than in one from which it has not, and 
the more nearly the air is exhausted the longer the motion 
will continue. So much for the influence of the air; but 
how about friction ? We cannot make any contrivance in 
which there is no friction at all; but every one knows what 
happens when we diminish it. The more slippery we make 
a surface the further things will slide upon it, and the more 
we diminish friction in wheels and pendulums by lubricants 
or special bearings the longer they will keep on moving. 



292 METHOD OF CONCOMITANT VARIATIONS. 

If friction did not affect the continuance of a movement, a 
vast number of influences that agree in nothing else but the 
diminution of friction would not all agree in prolonging the 
movement. Thus we can use the Method of Concomitant 
Variations to prove that the resistance of a surrounding 
medium and friction help at least to make things stop 
moving. 

To take another illustration of the same method. Suppose 
that things weighed on an extremely delicate spring balance 
seem lighter and lighter, or that pendulums swing more and 
more slowly, the farther we take them on a mountain or in 
a balloon, away from the centre of the earth, no matter 
which side of the earth we may be on or where the earth may 
be in its orbit. If the experiments are tried with proper 
precautions, the distance from the centre of the earth is the 
only condition that is varied alike in all of them, and the 
continual variation in this one respect is invariably accom- 
panied by a corresponding variation m the downward pull 
of everything we try, whether we measure that pull by its 
effect upon the spring in the balances or by its effect upon 
the rate at which the pendulum swings. From this we have 
a right to conclude that the nearness of the earth, and there- 
fore the earth itself, has at least something to do with the 
tension exerted by a weight upon a spring and with the 
swinging of a pendulum — and perhaps with the general 
tendency of things to fall. 

MilTs canon for the method is as follows: 

*' Whatever phenomenon varies in any manner whenever some 
other phenomenon varies in some particular manner is either a 
cause or an effect of that phenomenon^ or is connected with it 
through some /act of causation. 

The last clause m the canon is intended to cover cases 
where two phenomena have corresponding variations, not 
because one causes the other, but because they both depend, 
at least to some extent, upon some third variable which 
perhaps has not been observed at all. If we could be sure 



CAUTIONS. 293 

that there were only two variables, we could be sure that 
one of them was the cause, or at least a part of the cause, of 
the other. Because we cannot be sure that one of the 
observed variables is the cause of the other until we are sure 
that there is no third variable to play this part the Method 
of Concomitant Variations is at bottom, like all the other 
inductive methods, one of exhaustion. 

So much we can infer according to the Method of Con- 
comitant Variations if we take account of only the mere fact 
of change. If we know and take account of its amount also, 
we can often go further and find out with more or less cer- 
tainty how much the one variable has to do with the other: 
whether it is the complete cause or only a part of the cause, 
and what is the mathematical relation between the cause and 
the effect. For example, if we know that the income of a 
certain agent always increases as his sales increase and 
diminishes as they diminish, we may infer from this that at 
least a part of his income is derived from a commission on 
sales; but that is all. On the other hand, if our information 
is more definite, and we know that when the sales are 
doubled or quadrupled the income is also doubled or quad- 
rupled, we shall probably be correct in inferring that the 
whole income is derived from a commission on sales, and of 
course we can tell what the commission is. If we know that 
when the monthly sales amount to $10,000 the income is 
$280, when they amount to $20,oco it is $480, and when 
they amount to $40,000 it is $880, we shall be able to guess 
that the agent has a salary of $80 a month and a commission 
of two per cent on his sales. 

In reasoning of this sort, however, there are two things 
about which we must be very careful. In the first place, 
where there are only a few data they are often 
consistent with any one of several laws of rela- 
tion, and we cannot be absolutely certain that the one we 
happen to hit upon is correct. To take the case just given: 
the figures would be explained just as well if we supposed 



294 METHOD OF CONCOMITANT VARIATIONS. 

that instead of receiving any salary the agent paid his prin- 
cipals $120 a month for his office or his ' outfit ' or the use 
of their name, and received in return a commission of four 
per cent on all sales up to $10,000 a month, and two per 
cent on the balance; and it might be that if we thought 
about the matter long enough we could find still a third 
arrangement that would explain our data just as well as 
either of these. 

The other thing to be careful about is not to assume that 
the law found to hold within certain limits will necessarily 
hold when we get very far beyond them. If we had enough 
more data which made it practically certain in the case we 
have been considering that the agent had a salary of $80 a 
month and a commission of two per cent, this would not 
prove that he would still continue to get a salary if he made 
no sales at all, nor yet that he would continue to get two 
per cent on all his sales if their number were very largely 
increased. It might very well have been agreed that on all 
sales over, let us say, $50,000 a month he should get a com- 
mission of only one per cent. In the same way, we may 
have noticed that the more wind there is the more work it 
is possible to get out of a windmill ; but that is no reason 
for believing that the best results of all would be had in a 
hurricane, where the mill might break down altogether. 
We can never tell how far we are away from a point at which 
some new relation enters in to upset all our calculations. 

In spite of the necessity for these two precautions, the fact 
that there are many cases in which the amount of variation 
can be measured makes this method particularly useful. 
*' Although the most striking applications of the Method of 
Concomitant Variations takes place in the cases in which the 
Method of Difference, strictly so called, is impossible, its use 
is not confined to those cases; it may often usefully follow 
after the Method of Difference, to give additional precision 
to a solution which that has found. When by the Method 
of Difference it has first been ascertained that a certain 



CAUTIONS. 29s 

object produces a certain effect, the Method of Concomitant 
Variations may be usefully called in, to determine according 
to what law the quantity or the different relations of the 
effect follow those of the cause/' * 

When the Method of Concomitant Variations is used in 
this way to give precision to causal laws, it is obvious that 
it rests no longer upon the bare assumption that every event 
has a cause, but upon the more refined assumption that the 
amount of the cause is related to the amount of the effect by 
some law of definite proportion. 

^ Mill : Bk. Ill, Chap. VIII, Sec. 6. 



CHAPTER XXX. 

GROUP COMPARISONS, OR THE METHOD OF STATISTICS. 

In the examples already given, the Method of Concomitant 
Variations was applied in the following way. We noticed 
the state or action of some individual thing, then introduced 
a change into the surroundings and noticed what change 
followed in the state or action of the same individual. We 
compared the time which it takes for a pendulum principle 
to make a complete oscillation (or a hundred ^^^^^^^s. 
continuous oscillations) when it is swung at the level of the 
sea and when it is swung at various distances above it, or 
we compared the distance that a spring is stretched or 
twisted by some heavy object attached to it at the level of 
the sea and at various distances above it. In all the experi- 
ments necessary for such comparisons we swung the same 
pendulum or weighed against our spring the same lump of 
lead. This, however, was not absolutely necessary. If we 
were quite certain that two pendulums or two lumps of lead 
were exactly alike in every essential respect, we could use one 
at the level of the sea and the other at the mountain-top, 
and still draw our conclusion from the difference in the 
results. But whether the individuals compared were identi- 
cal or not, in either case we compared the states or actions 
of single individuals. Moreover it will be remembered that 
to draw any conclusion from the results of such a compari- 
son we had to be sure that the change in elevation was the 
only change made that might affect the downward pull in 

296 



PRINCIPLE AND USES. 297 

question. If that downward pull had been subject to varia- 
tion from a hundred other causes known and unknown, 
whose influence we could not possibly estimate, then the 
' experiment could have told us nothing about the effect upon 
that pull of the changed distance from the centre of the 
earth. 

In cases of this latter sort inferences that cannot be based 
upon what happens m the case of a single mdividual can be 
based upon the total or average change produced in a very 
large number. We know, for example, that the growth of 
a child as measured by its weight depends not only upon its 
age, but also upon a vast number of other influences: its 
own natural vitality, the size of its parents, the nature and 
amount of its food, the amount of sunlight and fresh air to 
which it is exposed, its freedom from disease, its exercise. 
Its happiness, and so on ; and we cannot possibly tell how 
much influence any one of these has exerted upon the growth 
of an individual child. Consequently we can tell very little 
about the growth due to age by weighing a child when it is 
six and again when it is seven; much less by comparing the 
weight of one child of six with that of another child of seven. 
Yet if we compare the average weight of several thousand 
children of six with that of several thousand children of seven 
selected in the samiC way from the same neighborhood, then 
w^e shall have a right to infer that the difference in the 
average weights is due, to a fraction of one per cent, to the 
difference in age. If one child of seven has attained its 
growth under better conditions than some child of six, there 
is undoubtedly some child .of six that has attained its growth 
under better conditions than some child of seven; so that on 
the w^hole the favorable and the unfavorable influences m the 
two groups are balanced evenly enough to be disregarded. 
Thus by comparing large enough groups we can often 
eliminate the effects of all the causes but those under con- 
sideration and get a very accurate measure of the effect 
exerted by the latter. 



^gB GROUP COMPARISONS. 

This Method of Group Comparison is used very commonly 
at the present time, especially in physiology, psychology, and 
economics, to estimate the effect of various influences that 
cannot possibly be isolated from a great many others, and 
whose results cannot be estimated with accuracy in any other 
way. To take a practical example. 

Is there any connection between a child's size, as distin- 
guished from its age, and its mental development ? We 
should be able to answer this question if we can find out 
whether large children are better developed mentally than 
smaller children of the same age, or, what amounts to the 
same thing, whether children of better mental development 
are larger on the whole than children of the same age of 
poorer mental development. To find this out an investi- 
gator takes through the teachers of a large city the ages and 
weights of some thirty thousand pupils in the public schools. 
He then finds the average weight of all the pupils of the 
same sex and age throughout the schools, as well as the 
average weight of all the pupils of the same sex and age in 
each ' grade '. Comparing these averages together he finds 
that in practically every case children in higher grades weigh 
more than children of the same age and sex in lower grades. 
Accepting the progress which a child makes in school as a 
fair enough test of its mental development, and the grade in 
which it is found as a fair enough test of its progress, he 
concludes from this that children with greater mental 
development are on the whole larger than children of the 
same age with less mental development."^ From such a 
conclusion, rightly established, we should have a right to 
infer that a child's mental development depends not merely 
upon its age, but upon the development of its body, or, 
conversely, that the development of the body depends not 
merely upon age, but upon the development of the mind, 
or else that the development of the mind and the develop- 

■^ See Transactions of the Academy of Science of St. Louis, Vol. VI, 

No. 7. 



PRINCIPLE AND USES. 299 

ment of the body both depend largely upon the same con- 
ditions; in short, that there is a close causal relation between 
them. 

Here is an example of the measurements: 

Average weight of 2188 boys nine years old 57.41 lbs. 
'' " '' the 570 of these in Grade I 55.52 " 

«< a a a jj^^ a a a a H 57-56 *' 

n u a a 257 " '' " '* III 59.26 " 

<< a n ii ^^ a a a a W 61.9I *' 

Twenty-two boys out of the total of 2188 who were meas- 
ured are not accounted for in this table. These twenty- 
two boys must have been in the Kindergarten and the grades 
higher than the fourth. Their measurements are not aver- 
aged because the investigator thought, very properly, that an 
average could not be depended upon unless it were based 
upon at least twenty individual measurements. 

The table shows a difference in weight of about two 
pounds between boys of nine in one grade and those in the 
grade above it; so that between the boys of nine in the first 
grade and those in the fourth there is the very decided differ- 
ence in the average of over six pounds. The very consider- 
able size of these differences, the almost unbroken regularity 
with which they appear from one grade to the next, not only 
with boys of nine, but w^ith both boys and girls of all ages 
between six and sixteen or seventeen, and the large number 
of total measurements, to say nothing of certain other rela- 
tions brought out in the original article, — all these prove 
that the different average weights in different grades cannot 
be the result of mere chance — that there must be some real 
cause at work which tends to make the boys or girls of a 
given age in a higher class heavier than those in a lower 
class. In this way, by comparing the average measurements 
of several large groups we can often prove the existence of 
causal relations which we could never prove by merely com- 
paring a few individuals. 



300 GROUP COMPARISONS. 

The errors to which we are liable in such investigations as 
this are very serious. In the first place we must make sure 
Number of ^^^^ enough measurements are made to eliminate 
data. the effects of purely individual idiosyncrasies. 

One boy with twenty pounds of extra fat would make a 
difference of two pounds in the average when he is one of 
only ten; but he makes a difference of only one fiftieth of a 
pound when he is one of a thousand. In general, the larger 
the groups from which we get our averages, the less chance 
there is that the distribution of peculiar individuals will be 
uneven enough to make a difference worth considering in the 
results. In the table it will be noticed that the difference 
between nine-year-old boys in the third grade and those in 
the fourth is slightly greater than that between any other 
two successive grades. This extra difference might well dis- 
appear if instead of forty-four boys in the fourth grade to 
examine there had been a thousand. The accuracy with 
which we should read our averages always depends upon the 
number of measurements from which the average is com- 
puted. 

A second blunder to be avoided in statistical investigations 
where the data are supplied by different observers arises from 

what is called the ' Personal Equation ' of the 
Personal 

eauation, observers. Where there is any doubt about a 
etc. 

quantity some people constantly tend to over- 
estimate it, others to underestimate it. If one object or 
set of objects happens to be measured by a person who 
habitually overestimates, and another by one who habitually 
underestimates, it is evident that the difference between the 
two will appear a little larger or a little smaller than it 
really is. Personal equation of this general sort appears in 
many different forms. If each of two people has to press a 
button the moment he sees a certain sight or hears a cer- 
tain sound, the chances are that they will not both press it 
at exactly the same time. One will nearly always act a 
fraction of a second later than the other. The more praC' 



PERSONAL EQUATION, ETC. 301 

tice each of the two has had in this sort of reaction the more 
likely he is, not to be more accurate, but to be more con- 
stant in his error; and therefore the more likely it is that 
the interval between the reactions of the two observers or 
experimenters will always be about the same, so that proper 
allowance can be made for it. In this way two astrono- 
mers may always differ by perhaps a tenth of a second of 
time in the records which they make of the movements of 
the heavenly bodies; and before they come to put their 
results together they always find out what the personal equa- 
tion of each observer is and make due allowance for it. 
Another example of this general kind of personal equation 
is found in our different estimates of distance. In trying to 
find the centre of a horizontal line, some people habitually 
go too far to the right, others too far to the left; and when 
we are asked to estimate the relative lengths of a horizontal 
line and a vertical line which is actually precisely equal 
to it, almost everybody will say that the vertical line seems 
a little longer, but the error will be greater with some people 
than with others. 

There is a similar difference between people in the use of 
words whose meaning is rather vague. If we are comparing 
the amount of drunkenness in different cities, we must be sure 
that the persons who collected the statistics all defined the 
term in the same way. It may be that in one city a man 
was called drunk when he had imbibed enough alcohol to 
make him noisy, in a second when he staggered, and in a 
third not until he fell down. The terms ' sick ', * typhoid 
fever ', ' pauper ', * criminal ', ' morbid ', and a host of others 
are subject to variations of this sort in their definition. 

In comparing the official statistics of different places or 
periods we must be careful to see not only that the terms are 
defined in the same w^ay in them all, but also to see that 
about the same proportion of actual cases are reported. In 
some places a much larger per cent of the actual births, 
contagious diseases, or crimes is reported than in others. 



302 GROUP COMPARISONS. 

Much the easiest way for a police department to diminish 
disorderhness — on paper — is to instruct the patrolmen to 
report as few cases as possible. 

Another source of error, very much like personal equation, 
is due to preconceived opinions on the part of the observers 
as to what the result of the investigation should 
tionsand be. This danger is especially likely to affect 
statistical inquiries that depend upon data fur- 
nished by a set of observers untrained in that kind of work. 
But it is hard enough for any one to avoid, even in taking 
what we call exact measurements. No measurements are 
absolutely accurate; and if it is a question of whether some- 
thing measures 26. 2 units or 26.3 our decision is likely to be 
influenced more than we realize by the desire to give our 
theory the benefit of the doubt. Hence it is advisable to 
take each measurement in such a way that it is impossible 
to tell which side of the question it will help until it is not 
only taken but recorded ; and after we do know its bearing 
it should not be subject to revision. When the measure- 
ments are taken by assistants untrained in such work it is 
wise to begin with a small preliminary investigation in order 
to make sure that the instructions are absolutely full and 
clear, and in many cases it is also desirable to exclude any 
possible influence of prejudice by leaving the assistants in 
complete ignorance as to the question at issue, though this 
should not be done if they will imagine that the issue is 
something else in which they are more interested. 

This effect of prejudice upon our measurements is not 
confined of course to group comparisons. It is found every- 
where. Every teacher knows how much easier it is to grade 
an examination paper fairly when he does not know who 
wrote it than when he does. A phrase used by a good 
student may suggest all that he probably knows and thus 
get a high mark, while the very same phrase from a poor one 
suggests all his stupidities and gets a low mark. Hence the 
teacher who really means to be guided in making his grades 



PRECONCEPTIONS AND INTERESTS. 303 

by the face of the returns will try to read and mark the 
papers before he knows whose they are, and even to mark 
the answer to each separate question before he knovNS pre- 
cisely what effect that particular mark will have upon the 
unknown student's standing as a whole, e.g., whether it is 
or is not barely enough to pass him or to give him honors. 
The less strongly w^e feel the issues at stake the more 
accurately we are likely to judge. 

The effect of preconceptions and personal interests appears 
again in the selection of cases. If a teacher wishes to show 
how bad his class is, he will put more doubtful cases in his 
list of those who are disorderly or deficient than if he wishes 
to show how good it is. So with purely theoretical ques- 
tions. To go back to our old example. Suppose the ques- 
tion to be settled by weighing the children in the various 
grades had been hotly discussed by the teachers who 
afterwards took the weights. How natural it would be for 
some of them, unless they had most explicit instructions to 
the contrary, to omit the weight of this or that individual 
pupil on the ground that to include it in the set from w^hich 
an average is made w^ould be manifestly unfair! ' Johnny is 
very bright and very small; but then he is a cripple, and it 
is certainly not fair to include him '; ' Mary is a great big 
girl in the second grade, but they really should have let her 
into the third, so I will not include her'. If we begin in 
this way to include only the cases that seem to us reasonable, 
it is perfectly evident that our views of what is reasonable in 
any particular case will depend very largely upon what w^e 
think beforehand about the question at issue; and as the 
result of the whole investigation will be influenced by our 
decision in these particular cases, there is always a strong 
tendency for the investigation to merely confirm the opinion 
we had to begin with. For this reason it is always desirable 
to lay down rules of procedure beforehand that leave no 
room whatever for selective judgment during the course of 
the investigation. Undoubtedly it often is unfair in making 



304 GROUP COMPARISONS. 

up an average to include exceptional cases. But the only 
safe way to overcome the unfairness is to base the average 
on so many cases that it will make practically no difference 
in that average whether a few exceptions are included or not. 
If any such large number of cases is not available, then the 
statistical method is not reliable. We appeal to statistics 
because we wish impartial witnesses instead of mere in- 
dividual opinions, and it is obviously absurd to run the 
slightest chance of selecting some of the witnesses because 
they will testify in our favor and excluding others because 
they will testify against us. 

However successful we may be in avoiding the influence 
of our own personal equation or that of others in the selec- 
Accidental ^^^^ ^^^ measurement of cases, we may still 
selection. choose our cases according to some plan that 
does involve an unfair selection though we do not realize it. 
The method of group comparisons is based on the assump- 
tion that the force under investigation is the only one which 
does not act about as much upon the members of one of the 
groups compared as upon the members of the other. But 
if this assumption is not correct, if some other force is present 
which really does act more upon the members of one group 
than upon the members of the other, and if we overlook its 
presence, it is clear enough that we shall attribute too 
much or too little to the force we are investigating; we sup- 
posed we had excluded all other constant causes, and we had 
not. 

Suppose, for example, whether it be true or not, that the 
further a child gets in school the better able he is either to 
help his parents at home or to earn money for them outside. 
It is evident that the poorest and most shiftless parents will 
be tempted to take their children out of school as soon as 
their labor is worth a very few cents a day; and unless the 
law is enforced very rigorously they will find means of doing 
so. Others less poor or less improvident will allow their 
children to go a little farther. This process would continue 



ACCIDENTAL SELECTION. 305 

from grade to grade, until in the high school nearly all the 
children represented homes that are fairly comfortable and 
well-ordered. It is evident that causes of this sort would 
produce a process of partial selection on some basis other 
than that of the children's individual mental development. 
Many of the children in the lowest grades would be paupers; 
those in the highest would not. In such a case it might 
well be that the difference in weight between children of the 
same age in lower and in higher grades is due, at least in 
part, to the fact that the latter come on the whole from more 
prosperous families, and are therefore better fed and cared for. 

If it should turn out upon investigation that there is 
nothing in this suggestion, we might offer another somewhat 
different. Suppose that amongst the most ignorant classes 
in a city there is for some reason or other a rather hostile 
feeling towards the public schools, so that the most ignorant 
parents keep their children out of them as long as they 
possibly can; while parents of the better classes, on the 
other hand, send them just as soon as they can. This would 
of itself tend to put children from the better homes in higher 
grades than those of the same age from the worse homes. 
Moreover, in the better homes children are helped with their 
lessons and encouraged to keep up with their class, or ahead 
of it, while in the worse they are not. In this way children 
who are better cared for at home, and therefore probably 
larger, would tend, apart altogether from any mental 
superiority of their own, to be farther along in school than 
those who are less well cared for at home. But there is still 
another, more direct, consideration in the case we have sup- 
posed. The smaller the child the longer can a parent 
prejudiced against the schools pass him off as too young to 
be sent; and the larger the child the easier it is for the 
intelligent parent who wants him to go to school to persuade 
the authorities that he is really mature enough to begin, even 
if he is not quite up to the legal age. 

If it is customary in the city in question to promote nearly 



3o6 GROUP COMPARISONS. 

all the children at the end of the year whether they have 
accomplished very much during the year or not, it is evident 
that a child's grade in the schools of such a city would 
depend far less upon his mental development than upon the 
age at which his school career happened to begin. Thus 
there might be a double or triple reason why large children 
should be farther along in school than small ones, apart 
altogether from any difference in their own mental develop- 
ment. 

When such objections as these are offered to the conclu- 
sions which any one draws from a set of statistics, the way to 
answer them is to find out by supplementary inquiries 
whether the causes suggested really are at work in the case 
in question ; and if they are, to estimate the amount of effect 
which they are likely to produce, and thus see how much of 
the total effect is left for the causes originally assigned. Until 
conclusions based upon the method of group comparison have 
been subjected to much critical examination of this sort, we 
must not attach to them anything like absolute confidence. 

Another danger which confronts this method of group 
comparisons — and indeed all methods that depend upon 
Misplaced precise measurements — is that we shall infer the 
accuracy. presence of some cause from numerical computa- 
tions that are far too precise for the data from which they are 
derived. By this I mean too precise for the least accurate of 
the data. When mathematicians take two sets of measure- 
ments which are to enter into the same problem, and when 
they can only get a certain proportion of accuracy in one, 
they realize that the inaccuracy of these data will affect the 
problem as a whole in the same proportion, and so they make 
no effort to get a greater degree of accuracy in any of the 
other data. For example, suppose we know that one side, 
B, of a triangle is twelve times as long as the base, A, and 
that we measure A for the sake of finding the length of B. 
If A is really loi inches long but we make it loo inches, 
that will mean that B is really loi feet long, though we cal- 



MISPLACED ACCURACY. 307 

culate that it is just 100 feet. In this way, an error of one 
inch in the length of A corresponds to an error of twelve 
inches in the length of B. If we measured both A and B for 
the sake of comparing them and did not try to measure A 
more accurately than in even inches, it would be a waste of 
time to measure B more accurately than in even feet. 
Moreover, it would be a positive blunder to say that A 
measured ' exactly ' 100 inches; that B measured ' exactly ' 
100 feet and i inch; and that B was therefore a little more 
than twelve times as long as A. If we measure B to an inch, 
we must measure A to a twelfth of an inch before we insti- 
tute any such precise comparisons between them, or draw 
any conclusion from the existence of such slight discrepan- 
cies. When we multiply a measurement we multiply the 
error that we made in taking it ; when we divide a measure- 
ment we divide the error. So in general we can say that 
any figure which has to be multiplied before it is added to, 
or subtracted from, or compared in any way with, another 
should be reached by more careful measurements than that 
other; while a figure which has to be divided before it is 
compared with another may be reached by less careful 
measurements than that other. 

To take another example of this law of proportion in the 
accuracy with which we should take various measurements. 
A certain horse trots a mile in about two minutes and five 
seconds. The stop-watches by which he is timed will 
register fifths of a second, but nothing less. If we wish to 
find his speed as accurately as possible, how accurately 
should w^e measure the course over which he trots ? A horse 
trotting at the rate given goes more than eight feet in a fifth 
of a second, and since the watches will not register any time 
less than a fifth of a second, they are absolutely incapable of 
measuring the time that it takes the horse to go eight feet or 
less. It would therefore be a waste of time to measure the 
course for such a horse to a fraction of an inch.* 

* Absurd, I mean, if we are measuring the track merely for the sake 



3o8 GROUP COMPARISONS. 

Indeed, the very precision of such measurement might be 
misleading. Suppose, for example, that horse A trots over 
the mile track in New York in two minutes and five and one- 
fifth seconds, and that horse B trots over the mile track in 
Toronto in the same time. Suppose also that accurate 
measurements show the Toronto track to be really six feet 
longer than the New York track. How natural it would be 
to say that since B went six feet farther than A in the same 
time, he must have gone faster! But this conclusion is abso- 
lutely unwarrantable; for when we say that the two distances 
were covered in ' the same time ' we mean that in each case 
the time was at least as much as 2.5! and less than 2.5|. 
In other words, we mean that the difference between the two 
was less than a fifth of a second. But with a possible differ- 
ence in the time of almost a fifth of a second it may be that 
A really trotted faster than B after all."^ 

In our example of group comparisons I think we find a 
blunder of this same sort. The other objections which we 
made to the conclusion based upon the weights of school 
children in different grades were largely hypothetical. This 
objection is real. The investigator's object is to find out 
what difference there is in the weights of pupils of the same 
age who are in different grades. In the tables which he gives 
for comparison the average weights are all calculated to the 
hundredth part of a pound. How accurate should he have 
been in finding the average ages ? If we take account of a 
difference in weight of one pound, should we not take 
account of a difference in age that is sufficient to produce 

of timing that particular horse with that particular kind of watch. The 
accuracy is justified by the fact that some time we may have a better 
watch or wish to time a slower animal. 

* It is absumed for the sake of simplicity in the argument that the 
stop-watch really will measure with accuracy to the fifth of a second^ 
When we remember that the starting and stopping of the watch depend 
upon human action in the midst of exciting surroundings, it is evident 
enough that there is still less accuracy in the measurement of the horse's 
time. 



MISPLACED ACCURACY. 309 

that difference of one pound ? If we take account of a 
difference in weight of one hundredth of a pound, should 
we not take account of a difference in age sufficient to pro- 
duce that difference of one hundredth of a pound ? How 
much is this ? 

According to the tables the average weight of all the boys 
examined who are eight at their nearest birthday is 52.39 
pounds; the average weight of all the boys who are nine at 
their nearest birthday is 57.41 pounds; and the average 
weight of all the boys who are ten at their nearest birthday 
is 62.38 pounds. This means that the boys gain about five 
pounds a year, or about a tenth of a pound a week, and the 
hundredth part of a pound in less than a day.* 

This law of average growth means that we cannot draw 
any conclusion from an average difference in weight of one 
tenth of a pound between two groups of children 'of the 
same age ', unless we have good reason to believe that the 
age really is ' the same ' not merely to a year but to a week. 
A difference of a week in age would account for a difference 
of a tenth of a pound in w^eight. In the same w^ay a differ- 
ence of ten weeks in age would account for a difference of a 
pound in weight, and a difference of twenty weeks for the 
difference of two pounds which the tables show between the 
boys of nine in any two successive grades. 

And now the question comes : Have we a right to believe 
that there is no such difference as this in the ages ? 

In the tables before us the children are grouped according 
to their age in years at their nearest birthday. No account 
is taken of months or days. In each group, then, there will 
be some children who are almost a year older than some 
others in the same group. But since it is fair to assume that 
there are about as many children a little under a given age 

* We assume here for the sake of simplicity that the growth is uni- 
form throughout the year. If we took account of the fact that it is not 
it would complicate the argument, but it would not affect the principle 
on which it is based. 



310 GROUP COMPARISONS. 

as a little over it, the average age of all the children called 
nine would really be almost exactly nine; and so with each 
of the uther ages. In this way we have a right to assume 
that the difference in average weight between all the boys 
called nine and all the boys called ten corresponds to a very 
definite difference in age of almost precisely one year. Thus 
this inference based upon the tables is perfectly correct, and 
we have a right to say that it really is a difference of one 
year in age which makes the difference of about five pounds 
in weight. 

This, however, is very different from saying that the boys 
called ten in any one grade are on the average a year older 
than the boys called nine in the same grade, or that the 
boys called nine in one grade are on the average precisely 
as old as the boys called nine in another. 

In fact the presumption is all the other way. A boy 
exactly eight years and six months of age is quite as likely 
to be in a grade with the boys of eight at their nearest birth- 
day as with the boys of nine; and a boy of eight years and 
seven months is almost as likely to be. On the other hand 
a boy of nine years and six months is quite as likely to be 
with the boys of ten as with the boys of nine, and a boy of 
nine years and five months is almost as likely to be. In this 
way one boy of nine might easily be two grades ahead of 
another, not because he is any better developed for his age, 
but merely because he is ten or eleven months older. And 
thus, in general, there is every reason to believe that the boys 
of a given age in a higher grade are considerably older on the 
average than those * of the same age ' in a lower grade ; and 
the difference in age might well account for a large part of 
the difference in weight. It could not account for a differ- 
ence of five pounds, of course; for the difference in age must 
always be less than a year. Hence it could not account for 
all the difference which is found betvv^een boys of nine in the 
first grade and those in the fourth; but it might account for 
enough of it to make the conclusion that bright children are 



MISPLACED ACCURACY. 31I 

larger than dull ones extremely doubtful. Precisely how 
much the actual difference in age really will account for we 
cannot tell until the age of each child is taken accurately 
enough to show precisely what this difference is. 

There is a difference between this example of conclusions 
too precise for the data upon which they are based and the 
one given before it. When we compared two individuals 
and concluded that the horse B was faster than the horse A 
because it trotted a few feet farther ' in the same time ', our 
conclusion may have been wrong, but it may also have been 
right, since the times really may have been the same. But 
in this other case when we compared several groups of indi- 
viduals and said that the members of one were so much 
heavier for their age than the members of another, our con- 
clusion was certainly wrong, since there is every reason for 
believing that the average ages of the members of the differ- 
ent groups were not at all the same. When the investigator 
compared the average weight of all the boys of one age with 
that of all the boys of another he had a perfect right to take 
the age of each individual very much more roughly than he 
would have done if he had been comparing two individual 
boys, because he had good reason to believe that the in- 
accuracies would balance each other. In this the method 
of group comparisons has a great advantage. But the very 
fact that the inaccurate measurements were good enough for 
one set of comparisons made him take for granted that they 
were good enough for another. Thus the peculiar advantage 
possessed by this method of group comparisons may conceal 
a great danger. 



CHAPTER XXXI. 

MEANS, OR AVERAGES. 



In the last chapter we had occasion to show how an infer- 
ence could be based upon a comparison of averages. Aver- 
ages are used so much in various kinds of reasoning that a 
few definite statements should be made about them. 

^ ^ The first vague notion of an average, as we now under- 
stand it, seems to me to involve little more than that of a 
something intermediate to a number of objects. The objects 
General niust of course resemble each other in certain 

conception. respects. Otherwise we should not think of 
classifying them together; and they must also differ in 
certain respects, otherwise we should not distinguish between 
them. What the average does for us, under this primitive 
form, is to enable us conveniently to retain the group to- 
gether as a whole. That is, it furnishes a sort of representa- 
tive value of the quantitative aspect of the things in question, 
which will serve for certain purposes to take the place of any 
single member of the group. ""^ In this respect an average is 
somewhat, though not precisely, like a general name. '^The 
ordinary general name rests upon \i.e., is used to mark] a 
considerable variety of attributes, mostly of a qualitative 
character, whereas the average, in so far as it serves the same 
sort of purpose, rests rather upon a single quantitative attribute. 
It directs attention to a certain kind and degree of magnitude, 

* John Venn, '» The Logic of Chance ", 1888, pp. 436 ff. 

312 



VARIOUS KINDS. 31 3 

'^We can easily see that the number of possible kinds of 
average, in the sense of intermediate values, is very great ; 
is, in fact, indefinitely great. Out of the general conception 
of an intermediate value, obtained by some treatment of the 
original magnitudes, we can elicit as many subdivisions as 
we please, by various modes of treatment. There are, how- 
ever, only three or four which for our purposes need to be 
taken into account. 

^^In the first place there is the arithmetical average or 
mean. The rule for obtaining this is very simple : add all 
the magnitudes together, and divide the sum by their number. 
This is the only kind of average with which the unscientific 
mind is thoroughly familiar. But we must not let this sim- 
plicity and familiarity blind us to the fact that there are defi- 
nite reasons for the employment of this average, and that it 
is therefore appropriate only in definite circumstances. ' ' 

The Arithmetical Mean of a series of quantities is that 
quantity which can be substituted for each one of them when 
they are to be added together, and produce the same sum. 
Six is the arithmetical mean of 4, 5, 7, 8, various 
because the sum of these four numbers and the ^^^^s- 
sum of four sixes is the same. Hence ^^for many of the 
ordinary purposes of life, such as purchase and sale, we 
come to exactly the same result, whether we take account 
of"* the exact size of each separate quantity and the differ- 
ences between them, or suppose each one of them to be equal 
to the average. If we are paying for melons by the pound it 
makes no difference in the price whether the dealer says that 
we bought one which weighed 4 pounds, one which weighed 5, 
one which weighed 7, and one which weighed 8, or whether 
he says we bought four that weighed about 6 pounds apiece, f 

The next kind of mean, or average, to be considered is the 
Geometrical It is that quantity which can be substituted 

■^ John Venn, loc. cit. 

f The arithmetical mean is the simplest case of the mean which is 
obtained by the method of least squares. 



3^4 MEANS, OR AVERAGES. 

for each one of several quantities when they are multiplied 
together, and give the same product. In this way 4 is the 
mean between 2 and 8, for w^e get 16 whether we multiply 2 
by 8 or 4 by 4. In the same way 6 is the geometrical mean 
of 2, 4, 27. The rule for finding the geometrical mean be- 
tween any number (n) of quantities is to multiply all the 
quantities together and find the nth. root of the product.^ 

Whether in any case we should use an arithmetical or a 
geometrical mean depends altogether upon the relations which 
we are considering between the things in question. If they 
are merely added together to produce an external result, like 
weights in the pan of a balance or like the simple interest 
which different sums of money earn in the same year, then it 
is clear from the definition of the arithmetical mean that we 
should use it ; but if the quantities are thought of as bearing 
some fixed ratio to each other and depending upon each 
other Hke the earnings of a sum of money from year to year 
at compound interest, then it is clear from the definition that 
we should use the geometrical. If it is not certain what the 
essential relations in question really are, then it is not certain 
which mean should be chosen. In the ten years from 1890 to 
1900 the population of Cleveland increased from 261,353 to 
381,768. That is, it gained 120,415 people, or a trifle over 
46^. Shall we take the arithmetical mean, and say that this 
represents an average increase each year of 12,041; or shall 
we take the geometrical, and say that it represents an average 
increase each year of 3.86^? The two means are quite dif- 
ferent. If we take the arithmetical, we think of an addition 
of precisely the same number of inhabitants each year ; if we 

* The geometrical mean of two quantities is often defined as ' a 
mean proportional between them ', or that quantity which bears the 
same proportion to the one as the other bears to it. According to this 
definition 4 is the mean between 2 and 8, because 2 : 4 : : 4 : 8, — not be- 
cause 2X8 = 4X4* Mathematically the two definitions amount to 
the same thing ; but the one given in the text is better for the purposes 
of logic. 



VARIOUS KINDS. 315 

take the geometrical, we think of a considerably smaller abso- 
lute addition (viz., 10,088) in the first year of the ten, when the 
city is comparatively small, than in the last year of the ten 
(viz., 14,159), when it is considerably larger. Which mean 
we should choose is simply a question of which we believe 
will best represent the facts. If the growth of cities depended 
altogether upon the birth of children within their boundaries, 
we should naturally choose the geometrical mean, for the 
larger the city (other things being equal) the more children 
will be born in it. If, on the other hand, the population 
of a city, like that of a prison or a hospital, were made up 
altogether of certain kinds of people who were sent there from 
without, there would be no reason why a large city should 
gain more inhabitants than a small one ; and the more appro- 
priate average would be the arithmetical. With most cities 
the natural rate of growth is only partly geometrical and only 
partly arithmetical ; so that neither a series of means of the 
one sort nor a series of the other would give a wholly satis- 
factory representation of the mean growth from year to year 
between one census and another. If in any case or set of 
cases we have reason to believe that the true mean lies some- 
where between the arithmetical and the geometrical, and if 
we wish to represent the facts as accurately as they can be 
represented by any mean, we must make a mean that does lie 
between the two.^ 

For many purposes the best mean to choose is not an aver- 

^ In estimating the population for any given time on the basis cf a set 
of census returns mathematicians actually use a set of equations like 
this: p = a ^ bt -\- ct'^ -\- dt'^ -\- etc., where/ is the population at some 
given time (different in the different equations), and / is the number of 
units of time (e.g., decennial periods) from any starting-point to the time 
of the population/. The values of «, b^ <:, d^ etc., are found from these 
equations, in v^hich the value of p is known, by the method of least 
squares; and then the value of/ at any other time can easily be calcu- 
lated. 

This formula actually does represent a rate of increase lying some- 
where between an arithmetical and a geometrical progression. 



3i6 MEANS, OR AVERAGES. 

age in any mathematical sense of the word at all, but simply 
the size or kind that occm-s most frequently. This is what 
is generally meant by the ' average man '. When we say that 
the average man likes a certain kind of newspaper or a certain 
kind of play, we siniply mean that the people who like that 
kind of newspaper or that kind of play are more numerous 
than the people who like any other kind. It does not mean 
that half the people in the community like something more 
refined or more intellectual and that the other half like some- 
thing less refined or intellectual. The ^ average man ' may 
happen to lie midway between two extremes ; but it is the 
numerousness of such men, not their middle position or any 
other such relation to other kinds of men, that the editor or 
the playwright cares about. 

Another kind of average, which is often quite good enough 
to represent a group for the purpose of comparing it with 
some other group, is what Mr. Galton calls the ' Median '. If 
we suppose all tlie objects in a group to be arranged in a row 
according to their size, the median size is the size of the 
middle object in the row. If we have to compare the size of 
the soldiers in an American regiment with that of the sol- 
diers in a Japanese regiment, we can measure all the men in 
each and take the arithmetical mean, if we wish to ; but it 
woula be much easier and it would answer the purpose quite 
as well to take the middle-sized man from each regiment and 
compare the two. The men in the middle make a better basis 
of comparison between the two regiments than those at eitlier 
end, because the size of the men who happen to be in that 
position is not affected so much by chance. In two regi- 
ments raised in the same place and in the same way the two 
men of middle size would be almost exactly of the same 
height ; but the men of extreme size might not, for one 
regiment might happen to contain a giant or a dwarf and 
the other not. 

Averages, or means, can be used for three distinct pur- 
poses^ some of which have been referred to already. 



FIRST USE OF AVERAGE. 317 

Averages can be used, in the first place, to settle the con- 
flicting claims of a number of different measurements of the 
same quantity. When we try to measure a thing ^.^^^ ^^^ 
very accurately we usually take the measurement of averag:e. 
at least twice, and when we come to compare the two or 
more measurements we always find, however carefully they 
have been taken, that there is some slight difference between 
them. This is true when we try to measure the side of a 
room to an eighth of an inch with an ordinary foot-rule, and 
it is true of the extremely careful measurements made with 
the best possible apparatus in a physical laboratory. Indeed, 
the more accurate we try to be, the more of these discrep- 
ancies we shall notice. In a case of this sort the chances 
are that any measurement which we accept as the true one 
will be wrong; but with this probability of being wrong, it 
is valuable to have a reasonable assurance that we are not 
very far wrong. Suppose that there have been ten measure- 
ments and that the smallest is 1038 and the largest 1043. ^^ 
we arbitrarily chose either of these extreme measurements 
as the one to go by, and if the measurement at the other 
extreme really happened to be right, then we should have 
made a blunder of 5 units ; if, on the other hand we chose 
some number about half way between them as the true meas- 
urement, then, if either of the extreme measurements were 
correct, the error would not exceed two or three units, and if 
the real quantity should lie between the two extremes, then, of 
course, the error would be still less. Thus, if we are recon- 
ciled to an error in our measurement but wish a reasonable 
assurance that the error is small, it is usually better to choose 
some kind of a mean measurement than one of the extremes.* 

* There are three principles which can be taken for granted when we 
try to find the true value of a quantity from a series of different measure- 
ments: (i) Positive and negative errors are equally probable; (2) There 
will always be more small errors than large ones; (3) Very large errors 
do not occur at all. To explain this last point. If I am measuring a 
wall with a yardstick and the record shows that according to each of the 



3i8 MEANS, OR AVERAGES. 

I say ^ usually ' because it is only usually that it is better. 
Choosing the mean is no infallible rule for getting certainty 
out of uncertainty ; and sometimes the blunderer who ac- 
cepts the first measurement that he takes comes nearer to the 
truth than the careful man who finds the mean of a large 
number. 

To take the mean of several estimates is a rule that might 
very well be carried farther than it is into every-day life. 
Too often we are guided by our last impressions, not because 
we have any reason to believe that the last is better than any 
other, but merely because it is the one which is present at 
the time when the final estimate must be given. A teacher, 
for example, examines a piece of work and marks it 5. The 
next day he examines it again and it seems to be worth 7. 
The chances are that this is the mark which he will hand in. 
What he should do under the circumstances is to treat him- 
self objectively ; to recognize that he had made two conflict- 
ing judgments ; to ask whether the conditions under which 
they w^ere made were any more favorable in the one case than 
in the other ; and, if they were not, to split the difference 
between them and mark the work 6. It is not true that ' first 
impressions are always the best ' ; but the saying would never 
have come into existence if people had not often blundered 
by ignoring them altogether. 

first four measurements it is somewhere between 102 feet 3 inches and 
102 feet 4 J inches, while according to the record for the fifth measure- 
ment it is 104 feet 3 J inches, it is perfectly evident that this last record 
is wrong. It could not have been produced by any combination of 
'errors' (such as slight variations in the length of the measuring- 
stick, in the accuracy with which it is placed and read, etc.). It is 
simply a mistake — I wrote down the wrong figure, or I made a mistake 
in my counting— and if it is not clear how the record can be corrected, 
the measurement must be disregarded. 

It is in accordance with all three of these principles that the mean is 
not only a safer measurement to accept than either extreme, as I have 
stated in the text, but also that it is far more likely to be substantially 
correct, though of course it is not certain to be, 



FIRST USE OF AVERAGE. 319 

Taking the mean of several measurements is not always 
the best way to find a quantity. In the first place, it is 
useless to take the mean of several measurements unless we 
can put up with the amount of error which such a proceed- 
ing will necessarily or probably involve. This error may be 
the one which is calculated from the differences between the 
individual measurements; it may be some constant error 
which probably exists and affects all the measurements, but 
for which we cannot make proper allowance because we do 
not know its amount and direction ; or a combination of them 
both. In the second place, we must not take the average 
of a set of measurements if we wish results which are as 
accurate as possible and if the measurements were taken 
carelessly and it is possible to take them over again more 
accurately. Finally, we must not take the average if we 
believe that there was some cause at work which prevented 
the errors from being scattered fairly evenly in both direc- 
tions, so long, at least, as there is any possibility of judging 
which direction ihe errors tended to take. We must not 
choose a mean between the measurements given by two 
individuals if we have reason to believe that one of them is 
dishonest or incapable, and, on the same principle, w^e must 
not choose the mean of several measurements if we have any 
reason to believe that the more skilfully a measurement is 
taken the more it approaches to one of the extremes. " In 
endeavoring to obtain a correct estimate of the apparent 
diameter of the brightest fixed stars, w^e find a continuous 
diminution in estimates as the powers of observation in- 
creased. Kepler assigned to Sirius an apparent diameter of 
240 seconds; Tycho Brahe made it 126; Gassendi, 10 
seconds; Galileo, Helvetius, and J. Cassini, 5 or 6 seconds. 
Halley, Michell, and subsequently Sir W. Herschel came to 
the conclusion that the brightest stars in the heavens could 
not have real discs of a second, and were probably much less 
in diameter. It would of course be absurd to take the mean 
of quantities which differ more than 240 times; and as the 



320 MEANS, OR AVERAGES. 

tendency has always been to smaller estimates, there is a 
considerable presumption in favor of the smallest." * 

The second use of averages is to find the mdividual which 
best serves as a type or representative of the species to which 
it belongs. In the case of averages like those that we 
Second use have just considered there was one true quantity 
of average, which we were trying to find. In this case there 
are many individuals of a given kind, each with a quantity 
of its own, and we wish to pick out one that will represent 
them all. A type of this sort is often doubly valuable; for 
in many cases (as with natural species) an individual lying 
about half way between the two extremes is not only a fairly 
good representative of each of them, but is also an excellent 
representative of a majority of the whole species, because 
men or horses or cats of medium size are very much more 
common than the very large ones or the very small ones. 
If a large number of men be arranged in a row according to 
their height, a line that just touched the tops of their heads 
would be about the shape of the black line on the next 
page.f There would be much more difference between the 
very tall man or the very short man at one end of the line 
and the man next to him than between any two successive 
men near the middle of the line. 

The reason for this is easily explained. Suppose that 
there are ten independent variables which together deter- 
mine a man's height; e.g., the height of his father as com- 
pared with the average of the species, that of his mother, 

* "Principles of Science", p. 390. — Instead of rejecting the poorer 
measurements entirely physicists sometimes 'weight' them, or admit 
them into the final reckoning in such a way that they do not affect it 
very much. What weights are to be attached to the various measure- 
ments — whether A's shall count for half as much as B's or only for a 
tenth as much — has to be determined arbitrarily, though there is a 
definite rule for determining the weights when they are made to depend 
wholly upon the number and probable error of the measurements in each 
of the series to be combmed. 

f After Bowditch. "Growth of Children ", etc, 22d An. Report 
of the State Board of Health of Mass. 



SECOND USE OF AVERAGE. 



321 



his own health during the period of growth, his food during 
that period, the amount of outdoor life which he had, the 
amount and regularity of his sleep, etc. Let us represent 
these different conditions by different letters from A to J ; 
let us suppose for the sake of simplicity that each of these 
conditions is either distinctly favorable or distinctly un- 




favorable; that each condition is as likely to be favorable as 
to be unfavorable; and that one favorable or unfavorable 
condition counts for as much as another. Condition A svill 
be favorable in one case out of two; and in cases when A is 
favorable B wdll be favorable in one out of two. That is to 
say, -A and B will both be favorable in only one case out of 
four. Similarly they wdll both be unfavorable in only one 
case out of four. But in one case out of four A will be 
favorable and B unfavorable, and in one case out of four A 
will be unfavorable and B favorable. Hence with only two 
variables there is one case out of four when both conditions 
are good; one when both are bad; and two when one is good 
and the other is bad. Working the problem out in this way 
we find that all ten conditions are favorable (or unfavorable) 
in only one case out of 2^^, i.e., in i out of 1024; but that 
cases in which some of the conditions are favorable and 
others unfavorable occur much oftener, and that the more 
evenly the favorable and unfavorable conditions are divided 



322 



MEANS, OR AVERAGES. 



the more frequently does the combination occur. Out of 
1024 cases 

10 conditions are favorable i time. 

10 tmies. 



9 






' 10 


8 






45 


7 






120 


6 






^ 210 


5 






' 252 


4 






^ 210 


3 






^ 120 


2 






45 


I 






* 10 



To students acquainted with the binomial theorem these 
figures and the process by which they are reached will be 
familiar. The mathematical law on which they are based 
represents the facts in most cases well enough to show how 
much more frequently things of medium size or quality are 
produced than those at either of the extremes. Thus the 
man of medium size or attainments is usually the 'average 
man ' in two or even three senses of the words. He is the 
man who stands in about the middle of the line; he is the 
commonest kind of man; and very likely the number that 
expresses his size or attainments is nearly the arithmetical 
mean of the numbers which express the size or attainments 
of all those in the group. 

Before we have a right to expect the arithmetical mean 
or the median of a group to be the commonest size or kind 
found in that group we must make sure that we are really 
dealing with one group of homogeneous things and not with 
several. If we measure a group of men half of whom are 
Americans and the other half African pygmies, the average 
height will be too small for the Americans and too large for 
the pygmies; and it might well be that not a single man m 
the whole complex group came anywhere near it. In the 
same way, if we should find the average size of all the articles 



SECOND USE OF AVERAGE. 323 

in a given room, from tables and lounges to pins and collar- 
buttons, there is no reason to think that things the size of 
the average — even if such things existed — would be any 
more common than things of any other size that any one 
might happen to think of. The things in the room are not 
homogeneous; and neither are the Americans and pygmies. 
To be homogeneous, in the sense in which the word is used 
here, things must be of the same general kind, — i.e., pro- 
duced by essentially similar groups of causes, — and the 
differences between them must be the ' compounded ' result 
of a large number of relatively independent conditions of 
approximately equal value. The articles in the room were 
not of the same kind at all; and in the case of the Ameri- 
cans and the pygmies the one condition of ancestry, different 
for the two groups, overshadowed all the rest. 

Even when the members of a group are perfectly homo- 
geneous it does not always follow that those of medium size 
or attainments are the most numerous. In a previous para- 
graph I said that m a regiment of soldiers arranged in line 
according to their height there might be a giant at one end 
of the line and a dwarf at the other. But if the soldiers are 
regular infantrymen recruited in time of peace, the dwarf 
would not be there, simply because the government refuses 
to accept recruits under a certain height. The well-marked 
curve at one end of the line which touches the men's heads 
is thus cut off, and in a regiment recruited in this way the 
commonest type of man would therefore be a little to the 
small side of the median and a little smaller than the 
arithmetical mean. So in any class at school or college, the 
students who are laziest and most stupid have been cut off 
by previous examinations; and consequently at the lower 
end of the class we do not find one person of extraordinary 
ineffectiveness, but rather a fairly large group who have 
barely succeeded in fulfilling the minimum requirements. 
Here also, therefore, the largest group is towards the lower 
end and somewhat below the arithmetical average. 



324 MEANS, OR AVERAGES. 

Another thing we must be careful about with averages of 
this sort is not to mistake the average for the ideal. If a 
child's growth is not up to the average, the physician has a 
right to suspect, though perhaps not to conclude, that 
something is wrong; but then the average by which the 
physician is guided is an average of children in good health, 
and then again it is only when the child's weekly growth 
falls below the average — not above it — that the physician is 
anxious. Thus he regards the average growth as a kind of 
minimum — not as the maximum to be striven for. So also 
with matters of conduct, the fact that ' everybody ' does a 
certain kind of thing is no reason in the world for believing 
that that is an ideal kind of thing to do. In the case of a 
race perfectly adjusted to its environment and incapable of 
further improvement it might be; but, as things stand, the 
commonplace of to-day is the ideal of yesterday, and the 
ideal of to-day is the commonplace, not of to-day, but of 
to-morrow. Another reason for striving for something 
better than the average in the case of conduct is this: The 
average is made up of good, bad, and indifferent; and if the 
best people in a community should suddenly cease to keep 
as far above the average as the bad are below it, the average 
would necessarily fall, and would keep on falling until the 
community went to pieces or until some one arose again 
who was willing to be better than the average of his fellows. 

The third purpose for which we find a mean is convenience 
in representation — to have " a merely representative num- 
Thirduse ^er, expressing the general magnitude of a series 
of average. ^^ quantities, and serving as a convenient mode 
of comparing them with other series of quantities", as in 
group comparisons. " Such a number is properly called the 
ficiitious mean or the average result. " * 

The average weight of the players in a football team may 

* W. S. Jevons, "Principles of Science " (1887), p. 359. The dis- 
tinction which Jevons here makes between the use of the words Mean 
and Average is not always observed, and I have ignored it in the text. 



THIRD USE OF AVERAGE. 325 

not come anywhere near the weight of any one of them, and 
it is not a kind of type towards which football-players tend; 
for there is reason why the quarter-backs should usually be 
lighter and the centres heavier. There is therefore no one 
thing in the world which the mean employed m this way 
represents or attempts to represent, and yet it has a real use 
when w^e consider the group as a whole in its relations to 
something beyond : in this case in relation to some other foot- 
ball teap and the chance of beating it. So w^hen w^e give 
the mean temperature of Winnipeg we do not mean to say 
that that is the commonest temperature there, nor yet that 
that is a kind of type which the temperature of each day 
naturally tends to approach; for we know that most days are 
either hotter or colder and that it is natural for days to be 
much hotter m summer and much colder in winter. But 
with reference to places and relations that lie beyond, a 
statement of the average temperature may be full of mean- 
ing. If the mean temperature of Winnipeg is lower than 
that of San Francisco, this means that for some reason or 
other it receives less heat from the sun in the course of a year, 
or radiates more away, or perhaps both; and if there is any 
process of growth or manufacture which depends upon the 
total amount of heat (regardless of variations from day to 
day) which Nature gives in the course of a whole year, a 
knowledge of the mean temperature of each place would 
tell which of the two w^ould be the more favorable in this 
respect. To quote again from Jevons: 

" Although the average w^hen employed in its proper sense 
of a fictitious mean represents no really existing quantity, 
it is yet of the highest scientific importance, as enabling us 
to conceive in a single result a multitude of details. It 
enables us to make a hypothetical simplification of a problem, 
and avoid complexity without committing error. The 
weight of a body is the sum of the weights of infinitely small 
particles, each acting at a different place, so that a mechan- 
ical problem resolves itself, strictly speaking, into an infinite 



32 6 MEANS, OR AVEkAGES. 

number of distinct problems. We owe to Archnnedes the 
first introduction of the beautiful idea that one point may 
be discovered in a gravitating body such that the weight of 
all the particles may be regarded as concentrated in that 
point, and yet the behavior of the whole body will be 
exactly represented by the behavior of this heavy point. 
This Centre of Gravity may be within the body, as in the 
case of a sphere, or it may be in empty space, as in the case 
of a ring. Any two bodies, whether connected or separate, 
may be conceived as having a centre of gravity, that of the 
sun and earth lying within the sun and only 267 miles from 
its centre. ' ' * 

While averages of this sort can represent the individuals 
in a group for certain purposes, it is only as members of the 
group. The average weight of the men in any athletic team 
IS nothing more than the figure obtained by dividing the 
total weight by the number of players. The minute any one 
of them leaves the team that average ceases absolutely to 
represent him m any way whatever, and ceases at the same 
instant to represent the others either, whether individually 
or collectively. An average of this sort need not be in any 
sense either a representative of a single individual, or of a 
type towards which the individuals tend, or of an ideal. 
It is the mere product of an arithmetical process, useful for 
the estimation of certain outward relations of the things 
averaged. 

The term Expectation of Life as used in insurance is likely 
to lead to the confusing of the two ideas which we are here 
trying to distinguish. To the insurance company it means 
merely the average time that insurable people of a given age 
and sex continue to live. To the layman it is likely to mean 
the time that he, as an individual, will probably continue to 
live — a very different thing, which should be calculated in 
an entirely different way. 

*Jevons, op. cit., pp. 363-4. 



MEASURES OF ERROR. 327 

Often it is well to add to an average some indication of 
the accuracy with which the average represents the quantities 
whose average it is. Ten is the arithmetical Measures of 
mean between 9 and 11. It is also the arith- ®^^®^- 
metical mean between 5 and 15. But in the first case the 
average comes much nearer to each of the separate quan- 
tities than in the second. In the first case the difference 
between the average and each of the quantities averaged is 
only I ; in the second it is 5. When the average represents 
a large number of quantities, the simplest measure of the dif- 
ference between it and each one of the quantities averaged is 
the average variation of the separate qua?itities from that aver- 
age. The arithmetical average of the variations is found by 
finding the difference between the average and each one of 
the separate quantities (regardless of whether that quantity be 
larger than the average or smaller), adding all these differ- 
ences together, and dividing by the total number of quanti- 
ties. Thus the average of 5, 6, 7, 11, 13, 8, 6, 20, 10, 14 
is 10 ; the separate variations from the average are respec- 
tively 5, 4, 3, I, 3, 2, 4, 10, o, 4; the sum of these separate 
variations is 36 ; and since there are ten quantities, the aver- 
age variation is 3.6. 

When we are dealing with a number of separate quantities 
'a knowledge of this average variation enables us to tell to 
what extent the average may be regarded as representative of 
each of them, and as thus serving the second purpose of an 
average, and to what extent, on the contrary, it must be re- 
garded as a purely fictitious quantity serving the third pur- 
pose only. Of course the smaller the average variation the 
more accurately the average represents the separate quantities 
averaged. 

When we are dealing with different measurements of the 
same quantity the average variation of the separate measure- 
ments from the average gives a measure of their accuracy. 
To be sure it does not tell anything about ^ constant ' or 
' systematic ' errors which affect all the measurements in the 



32 8 MEANS, OR AVERAGES. 

same way; but it does tell how much importance must be 
attached to * accidental ' errors, or those which result from a 
large number of different causes and are as likely to affect a 
measurement in one direction as in the other. The larger 
the average variation, the more important are these * acci- 
dental' errors and the less can we rely upon an average 
derived from a small number of measurements. 

This average variation is easily found, and it is a good 
enough measure of error for some purposes ; but mathe- 
maticians do not use it. What they do use is either the 
Median Error — generally known as the * Probable Error' — 
or the Mean Square Error. The former is commonly used 
in English-speaking countries, the latter in Germany. 

The Median Error, or so-called Probable Error, is the 
variation from the mean that half the separate measurements 
fall short of and the other half exceed. If we suppose all the 
separate measurements to be arranged in order of magnitude, 
the central quantity is the median, and the Median Error 
is the difference between that central quantity and the quan- 
tity half-way between it and the end of the line in either 
direction. The ' Probable Error ' is thus the amount of error 
that any one of the quantities is as likely to fall short of as to 
exceed. It is not the amount of error or variation from the 
mean that will probably be made. If we denote the differ- 
ence between each individual measurement and the mean 
(i.e., the ' errors' or 'residuals') by v^, v^, v^, etc., and the 
total number of measurements by n, the formula for finding 
the Probable Error (r) of a single observation is this : 

r z=z .6745 
or, more briefly, 




r=.6745'' ' '-''''^ 



V^. 



r 

The probable error of the mean, r^ , is -— . 

yn 



Measures of error, 329 

The formula for the Mean Square Error of a single meas- 
urement, e, or of the mean, e^, is the same as that for r or 
r^, except that the factor .6745 is omitted. 

The calculated error of a measurement is usually written 
after it, thus: 1287 ± 3. Unfortunately, however, this is 
ambiguous, for sometimes the error indicated in this way is 
the error of any one measurement out of a series, and some- 
times it is the error of the mean. By giving the latter where 
one expects the former an observer sometimes makes his re- 
sults appear more accurate than they really are. 

The student who wishes a fuller treatment of this subject 
is referred to Venn's ^^ Logic of Chance", to Jevons' 
'* Principles of Science ' ', or to some one of the many mathe- 
matical treatises on the theory of probability, such as Merri- 
man's or Comstock's. 



CHAPTER XXXII. 

PROBABILITY. 

In the last chapter we found that where several measure- 
ments or estimates do not agree it is often of practical 
advantage to assume that the truth lies somewhere between 
■^jjy them, and therefore to find out the average. We 

needed. found, however, that sometimes the nature of the 

case is such that an average is out of the question. If two 
people both claim the same piece of land, it would hardly do 
to say that each of them owns half of it; if one toss of a 
penny gives heads and another gives tails, there is no prac- 
tical purpose which will be served by assuming that the 
natural position of the penny is neither with heads up nor 
with tails up, but on its edge; if we do not know whether a 
certain act will please a person or annoy him, it will hardly 
do to assume that it will do neither one nor the other. In 
cases of this sort the mean is almost sure to be wrong, and 
so far wrong as to serve no practical use; it is therefore 
excluded and we have to choose between the extremes. The 
theory of probability discusses this choice. 

To the ordinary human mind and to all of the brutes this 
choice between extremes is often more natural than the search 
for a mean. If we do not know whether to fight a certain 
enemy as hard as we can or to run away from him as hard 
as we can, it is usually better to do one or the other — no 
matter which — than to follow the middle course and sit still 
and wait to be devoured; and, fashioned as we are for the 

330 



WHAT IT IS NOT. 33 1 

world in which we live, it is more likely that we will. If a 
friend is accused of playing us false, we may believe the 
charge, we may indignantly reject it, or we may alternate 
between these two extremes; but we are not likely at the 
time to assume that he was partly true and partly false or to 
take an attitude of perfectly neutral doubt. We are natu- 
rally partisan, and even when we seem to be calmly halting 
between two opinions we are generally not halting at all, but 
uncomfortably oscillating from the one to the other. Thus 
not only is it often perfectly rational, but it is also perfectly 
natural, to choose and accept as true some one of several 
incompatible alternatives, and it is the business of a logical 
theory of probability to show the kind of ground on which 
we can justify the choice of any particular one to the exclu- 
sion of the rest. 

When we toss a penny we say that heads and tails are 
equally ' probable ' or equally ' likely ' — that ' the chances ' 
are even; and when we throw dice we say that double sixes 
is ' improbable ' or * unlikely ' — that * the chances ' are 
against it. What do we mean by these words ' probable ' 
and * improbable ' and their equivalents ? 

Probability has sometimes been defined as a measure of 
belief. According to this definition, when we say that the 
chances are nineteen to one in favur of a certain what it 
event, we mean that we have some expectation i^not. 
of Its happening and some expectation of its not happening, 
but that the expectation of its happening is painted nineteen 
times as vividly upon the mind as the expectation of its not 
happening, so that w^hen the two pictures come back to us 
the one has nineteen times the force and vivacity of the 
other.* But if this were all that we meant by probability, 
the way to find out in any particular case what the chances 
or probabilities were would be merely to examine one's own 

* See Hume's "Treatise of Human Nature", Bk. I, Pt. HI, Sec, 
XXI, 



332 PROBABILITY. 

— or some one else's — mind and compare the strength of its 
various expectations. This, however, is not what we do, 
or rather it is not what we know we ought to do. When 
we want to get at the probabilities in a case we should 
examine the case, not our own feelings about it, and accept 
the result of this examination whether it agrees with our 
feelings or not. Of course we cannot examine things with- 
out having thoughts; but probability has to do, not with the 
thoughts, but with the things. 

Probability has to do with things; and yet it is not some 
mysterious inward power that strives to force them into a 
given course. We often speak of events happening ' by ' 
chance, as though chance were a real cause. "^ In the same 
way when we speak of the probabilities as favorable or 
unfavorable to a certain event, there is a tendency to think 
of these shadowy probabilities as allies or opponents of the 
event in question; and consequently when the physician 
says that ' the probabilities are slightly favorable ' we feel 
more like rejoicing than when he merely says that it looks 
now as though the patient might recover. The conception 
of probability as a kind of inward force striving to work itself 
out is called by Venn " one of the last remaining relics of 
[Scholastic] Realism, which after being banished elsewhere 
still manages to linger in the remote province of Prob- 
ability/' f 

* Of course Chance is never a cause, nor does the word imply the ab- 
sence of causes. '' We call a coincidence casual, I apprehend, when we 
mean to imply that no knowledge of one of the two elements, which we 
can suppose to be practically attainable, would enable us to expect the 
other, we know of no generalization which covers them both, except of 
course such as are taken for granted to be inoperative. In such an ap- 
plication it seems that the word 'casual' is not used in antithesis to 
' causal ' or to * designed ', but rather to that broader conception of order 
or regularity to which I should apply the term Uniformity. The casual 
coincidence is one which we cannot bring under any special generaliza- 
tion : certain, probable, or even plausible ". (Venn, 246.) 

•(• *< Logic of Chance ", p. 22, 



WHAT IT IS. SS3 

Hov/ then shall we define Probability without making it 

either a measure of belief or a mysterious force controlling 

thinsrs ? The only way is to keep the objective 

, - , J r , .T7, What it is. 

standpoint but get rid of the mystery. When 

we say that the probabilities are five to one against throwing 
six with a single die in any one throw, the only clear mean- 
ing we can have is this: that when dice are thrown a large 
number of times we get six in about one-sixth of the cases 
and something else in the remaining five-sixths. Conse- 
quently before we make the throw we can say that the 
probabilities are against turning up a six; and if when the 
throw is made we really do turn up a six, we can say that the 
improbable has occurred, but we ought not to say that our 
estimate of the probabilities had been erroneous, even though 
the guess we based upon that estimate was wrong. The 
only way to prove that the estimate of the probabilities was 
erroneous would be to show, either by direct experiment or 
from the nature of the causes involved, that in the long run 
of cases essentially similar to the one in question sixes are 
not turned up in about one case out of six. In the same 
way, when we say that a man of thirty will probably live a 
year longer, all we mean is that most men of his age and 
apparent health do live a year longer. We do not mean to 
say that this particular man will not die the very next day. 
If he really did die on the next day, we could say once more 
that the improbable had occurred and that our judgment of 
the probabilities was good in spite of the event. 

The statement that a thing may be improbable and yet 
occur is not absurd. When we throw a die the chances are 
always five to one against any one of the six faces, and yet 
we cannot help getting one of them. In the same way it 
is highly improbable that this, that, or the other individual 
who goes into a lottery will win the prize; and yet if it is an 
honest lottery, one of them must. In these cases the improb- 
able has to occur. Doubtless it is often said that if an event 
occurs, that very fact proves that it was not really improbable. 



334 PROBABILITY. 

and that if it does not occur, that proves that it was not 
really probable, although it may very well have seemed so. 
But when people speak in this way they use the word 

* Improbable ' as though it meant ' Impossible ', and the word 

* Probable ' as though it meant ' Inevitable '. 

Hence all that we mean by saying that a certain state of 
affairs is probable is that that state of affairs or something 
which is bound to bring it about actually exists in most cases 
of the sort. It does not mean that it will be found in that 
individual case. The outcome in the individual case is 
unknown, and all the words in the dictionary will not turn 
Ignorance into knowledge. 

But if the ' probability ' that we speak of with reference to 
a particular case really does not belong to that particular 
case at all, but only to the whole series or class 
of cases of which it is a member, what good does 
it do to think anything about it when the question at issue 
is not concerned with the series or class, but only with the 
individual case ? It may be very interesting to know that 
most men of thirty live another year; but what good does 
that do when the question is not about men in general, but 
about this particular man ? 

None whatever! — if the question at issue really does con- 
cern this individual case only. If a person is going to do 
only one risky thing in the whole course of his life, he might 
as well do it with his eyes shut as after a long calculation of 
probabilities. Some of the richest strikes in the world have 
been stumbled upon by fools and tenderfeet where wise men 
and experts have missed them. It is a pure risk. If we win 
we win, and if we perish we perish, and in the latter case it 
will not be much consolation to be assured that the good 
fortune we missed had once been ' probable '. Generally, 
however, the question is not of one case only. If we bet 
on dice, we usually mean to bet more than once and we are 
willing to lose many individual bets, provided the ' odds ' 
are so arranged that we win at least as much as we lose ir 



WHAT VALUE? 335 

the long run. If a company insures lives or houses or 
plate-glass windows at all, it tries to insure a great many and 
it expects a large number of losses. But it expects still 
more gains, and fixes rates that will make the total gains more 
than meet the total losses. In this way a business in which 
every single operation is extremely risky becomes on the 
whole one of the very safest and surest that a person can 
engage in. This is as true of professional gambling as it is 
of insurance — each single operation is as risky to the 
' banker ' as it is to the chance visitor; but if he only bets 
often enough and the chances are slightly in his favor, his 
winnings are bound to be greater than his losses in the long 
run. Now the conditions of life are so complex that, as all 
the proverbs tell us, "the best laid schemes o' mice and 
men gang aft a-gley'', and "nothing is certain but death 
and taxes ". We are engaged in operations which are more 
or less risky all our lives long. Therefore the only thing to 
do is to act in such a way that the gains will more than make 
up for the losses in the long run; that is, to take account of 
the relative frequency of the various different outcomes, and 
where odds — or the possible gains and losses in a single 
transaction — are even to act each time as though the most 
frequent outcome were going to be present then : to act 
* on general principles ' or ' according to the probabilities '. 
This way of acting on general principles is as natural as it 
is rational. Nature provided for it when she made us 
creatures of habit and imitation. It is inculcated in every 
maxim and moral rule. And because it is so natural as well 
as so rational to act in each particular case with reference 
to the general principle that will bring us out right in the 
long run, we come to feel that the general principle — whether 
it be a principle of morals or of probability — really means 
something for the individual case per se; and consequently it 
becomes almost impossible to get far enough away from its 
influence even in thought to realize that if there were only 
one uncertain situation in the whole world and a solitary 



33 6 PROBABILITY. 

human being who had to venture his life on one alternative 
or the other, the outcome would be with him a matter of 
mere unqualified luck, and the word ' probability ' would 
have absolutely no meaning. 

If probability belongs to an individual case only as a 
member of a class, so that an event may be improbable and 
still occur, why is it that the estimation of probabilities often 
Why hard seems so difficult, and what is the difference 
to estimate, j^etween good judgment in estimating them and 
bad judgment ? The difficulty which makes the difference 
between good and bad judgment so apparent is nothing 
more nor less than the difficulty of putting each individual 
case into the best class. The man of experience in any par- 
ticular line sees distinctions between things that the novice 
overlooks, and on the basis of these distinctions he can sub- 
divide his classes and estimate the probabilities in any par- 
ticular case by reference to the subdivision rather than to 
the larger class to which the case belongs. 

A stranger to the United States who happened to know 
that the two great political parties were nearly evenly divided 
would have to say that any American he met was just as 
likely to belong to the one as to the other. But a person 
who knew the country better would defer his judgment until 
he had found out in each case as well as he could what sec- 
tion of the country the person in question came from, what 
race he belonged to, what was his business, and so on. 
Every one knows that there is some danger in railroad travel, 
and, by comparing the total number of accidents in any 
given country during a given year with the total number of 
trains run, anybody can roughly estimate the chances of 
accident on some particular journey. But a man skilled in 
such matters might say that the road on which this particular 
journey was to be taken had a double track and block sig- 
nals and tests for color-blindness and this particular kind of 
brake and that particular kind of coupler, and that where 
they had all these things the proportion of accidents to trains 



CAUTION. 337 

— i,e., the * chance' of accident — was very much less than 
in the country at large. If he happened to know the records 
of the men who had charge of that particular train, he might 
form a more accurate estimate still. In the same way, a 
physicidTn examining an applicant for life insurance does not 
think of him merely as a person of a given sex and age who 
looks strong or delicate. He regards him as a person with 
a certain heredity, certain habits, certain lung capacity and 
heart action, and with or without symptoms of this, that, 
and the other definite disease. 

Such details do not tell how any given case will turn out; 
but they enable one to classify it with a small group of cases 
that resemble it quite closely rather than with a larger group 
that resemble it rather vaguely; and if the proportion of 
cases in which an event (such as a railroad accident) occurs 
or (if it is an event like death that must occur in every case) 
the average interval before its occurrence is something which 
we know as accurately for the smaller group as for the 
larger, this is a distinct advantage; for the greater the 
resemblance between all the individuals in a group the 
smaller is the variation between the outcome for any partic- 
ular case and the average outcome for the class. If we could 
find a past case that we knew to be absolutely similar to the 
one in question in every particular, and could thus base our 
judgment upon what we knew about a class of one, proba- 
bility would come to an end and we should have certainty. 
The greater our knowledge and skill the nearer can we come 
to such a class. Hence it is in the subdivision of classes 
and the knowledge of the outcome for each that the difficulty 
and the room for special skill come in. 

If probability is not a force and therefore exerts no influ- 
ence on the course of events, it is a mistake to believe that 

the non-occurrence of a probable event at one 

1 . Ti 1 Caution. 

time makes it any more likely to occur at 

another. If a person is tossing a coin and gets heads three 

times running, he is likely to say that next time it must be 



33^ PROBABILITY. 

tails. But this is a blunder. It is conceivable that one toss 
of a coin will affect another, just as a man's success in one 
enterprise may give him the confidence that leads to success 
or the overconfidence that leads to failure in the next. But 
if there is no such causal relation as this between the events 
themselves, probability is not going to become a cause and 
make one toss balance another. Whether we have tossed 
heads three times running or ten times, the coin will know 
nothing about it and the result of the next throw will be 
exactly what it would have been if no throws had preceded 
it at all. In the same way if a very improbable event occurs 
at one moment, that is no reason for believing that it will not 
occur again at the very next. Lightning is quite as likely 
to strike again in the same place (the proverb to the contrary 
notwithstanding) as to strike in any other given place of the 
same size. A second Galveston disaster is quite as likely to 
come exactly ten years after the first as to come exactly 137 
years and 48 days after. We are quite as likely to throw 
ten heads running as nine heads and then one tail, or any 
other precisely designated series.* 

The reductio ad ahsurdum of this view that events must 
balance and come out according to the probabilities is found 
in the story of the physician who said to his patient: 
' Madam, you can't help getting well; for the books say that 
one case out of every hundred does, and I have already lost 
ninety-nine. ' 

The mathematical calculation of probabilities is in the 
main very simple — so far at least as the underlying principles 
are concerned. If we are tossing a single die, we 
matica'l expect to turn up one face in the long run about 

princip es. ^^ often as any other, or, in other words, to turn 
up any given face in one-sixth of the total number of throws. 

* Of course a series is not precisely designated unless the order of the 
heads and tails is designated as well as their total number. ° Nine, heads 
and then one tail ' does not mean the same thing as ' nine heads and one 
tail ', for this last does not tell which one of all the ten throws the tail i^ 



MATHEMATICAL PRINCIPLES. 339 

We therefore say that the chance of getting that face — say 
the six — is ^. Since the ace and the six each occur in one- 
sixth of the total number of throws, one or other of them will 
occur in one-third of the total number; and so we say that 
the chance of getting either an ace or a six is \, and so on. 
It will be noticed in this case that the throw which gives any 
one of the six faces cannot by any possibility give any other; 
and so we can make some such general statement as this : 
Where two or more events are incompatible the chance of 
getting either one or the other is found by adding together 
the fractions which express the chances of each. Of course 
the chances against any given event or alternative are found 
by subtracting the fraction in favor of it from i. 

When we are tossing two dice (A and B) instead of one, 
we expect that in the long run each of the following com- 
binations will occur about as often as any other: 

AB AB AB AB AB AB 

1 21 31 41 51 61 

2 22 32 42 52 62 

3 '^ Z Z 1 43 5 3 63 

4 24 34 44 54 64 

5 25 35 45 5 5 65 

6 26 36 46 56 () (i 
With reference to the 6 or any other given face we can 

summarize these results as follows : 

A six and B six, i X -|- times = -gL- 

A six and B not six, i X f " = -3V 

A not six and B six, -f X -I- ** —3V 

A not six and B not six, | X f *' = If 

Total 11" 

Putting these results into more general form : "If the 

chances of a thing being p and a are respectively — and -, 

m n 

then the chance of its being both p and g is — , p and not 

mn 



34^ PROBABILltV. 

. n — 1 , . m — 1 , 

(7 IS , (7 and not p is , not p and not ^ is 

^ mn mn ^ 

[ffi \\\fi i^ 

^ — ' , where p and a are independent. The sum 

mn 

of these chances is obviously unity; as it ought to be, since 

one or other of the four alternatives must necessarily 

exist/' * 

One thing that a non-mathematician is liable to overlook 
in these figures is this, that the throws in which we get a six 
with either of two dice are not so common as the throws in 
Four more which we get either a six or an ace with one 
cautions. ^^^^ ^y^ Xyxxxi up as many sixes with the two 
dice as we turn up sixes and aces with one; but since the 
two sixes are on different dice and are therefore not in- 
compatible, they come together in one throw out of thirty- 
six, and we do not turn them up in so many separate throws. 
This explains the necessity for the word ' incompatible ' in 
the formula which w^e gave on page 339. 

A second thing to notice about the table has been already 
referred to in another connection : namely, that if we add 
together the numbers on the two dice in each throw, we shall 
find that one sum is by no means as common as another. 
Seven is the commonest, for it can be made by six different 
combinations; 6 and 8 next; then 5 and 9, and so on until 
we reach 2 and 12, each of which occurs only once. Thus 
once more the mean is commoner than the extremes. 

A third thing about these tables is worth dwelling upon 
because we are all likely to forget it when the figures are not 
before us: namely, the extremely small number of cases in 
which two independent improbable events coincide. Sixes 
with a single die are thrown in one case out of six, but 
double sixes with two dice in only one out of thirty-six, and 
if we should guess double sixes as often as they are thrown 
{i,e,^ one time out of thirty-six) the guess would be right 

* Venn, p. 174. 



FOUR MORE CAUTIONS. 34 1 

(i.e., coincide with the throw) in only one case out of 
36 X 36, i.e., in one out of 1296. To take another example 
of the same thing, if the chances of taking a certain disease 
are yi-^, and if a first attack neither increases nor decreases 
the liability to a second, the chance of a given person having 
that disease twice is only Yo-^-y-o. In other words, if one 
person out of 100 has it once, only one out of 10,000 will 
have it twice. The difference between these two figures is 
of course very striking, and any one who sees them is likely 
to forget about the mathematics and jump to the conclusion 
that a first attack affords almost complete immunity against 
a second. As Wallace says in his very ingenious (though 
by no means conclusive) article against Vaccination: " ' Very 
few people have smallpox a second time.' No doubt. 
But very few people suffer from any special accident twice — 
a shipwreck, or railway or coach accident, or a house on 
fire; yet one of these accidents does not confer immunity 
against its happening a second time. The taking it for 
granted that second attacks of smallpox, or of any other 
zymotic disease, are of that degree of rarity as to prove some 
immunity or protection, indicates the incapacity of the 
medical mind for dealing with what is a purely statistical 
and mathematical question. '' * Unfortunately " the medical 
mind" is not the only one that is likely to forget how 
rapidly fractions diminish when they are squared. 

The method of ascertaining causal relations by comparing 
the number of actual coincidences between two events or 
circumstances with the number that would naturally be pro- 
duced by mere chance according to the theory of probability 
is being used more and more as statistics of various sorts 
become more and more available; and by this method we 
must expect to reach many conclusions that seem at first, for 
the reason just given, to be contrary to all experience. 

A fourth word of warning about the interpretation of 

♦ Alfred R. Wallace, " The Wonderful Century ", N. Y., 189B. 



342 PROBABILITY. 

tables of probability. That an event turns out so many 
times in a given way is no reason why we should act that 
many times as though we expected it to turn out that way. 
On the contrary we should act each time as though we 
expected it to turn out in the most probable way. If we are 
guessing the total number of spots turned up by two dice 
and if we guess 7 every time, we will be right in 6 cases out 
of ^6, or 216 out of 1296. But if we should guess each 
number as many times as that number is actually turned up, 
we should be right in only 146 cases out of 1296, as the 
following table shows : 





T 


imes 


Times 


Times guessed 


nber. 


th 


rown 


guessed 


right 


: out of 36^ 


out 


of 36 


out of 36 


or 


1296 total 




th] 


rows. 


guesses. 


g 


uesses. 


2 




I 


I 




I 


3 




2 


2 




4 


4 




3 


3 




9 


5 




4 


4 




16 


6 




5 


5 




25 


7 




6 


6 




36 


8 




5 


5' 




25 


9 




4 


4 




16 


10 




3 


3 




9 


II 




2 


2 




4 


12 




I 


I 




I 



Total number of correct guesses 146. 

What is true in this case is true in any other: we should 
act each time as though we expected the most probable out- 
come to be found then. The figures show how much we 
can afford in the long run to risk upon each guess. ^ They 
do not show how many times in the long run each of the 
possible outcomes should be guessed. 



CHAPTER XXXIII. 
OBSERVATION AND MEMORY. 

Induction tries to weave facts together into a coherent 
world. But our knowledge of every one of these facts de- 
pends sooner or later upon a perception through the senses ; 
and if our ' senses deceive us ' and we perceive or think 
we perceive what is not really present, that false perception 
will tend to give us a wrong conception of the world. Hence 
it is necessary to know something about the difference be- 
tween good and bad perceptions. Moreover many of the 
perceptions from which we draw inferences took place some 
time ago, and if we depend upon our memory but do not 
remember them correctly, we are as badly off as if the percep- 
tions themselves were wrong. Hence we must consider 
memory also. 

The first thing to learn about Observation is the vast dif- 
ference between what one actually perceives and the inference 
by which he explains it. The word ^ Observa- 
tion ' seems to refer to the perception only ; but and infer- 
as it is generally used it includes a vast amount of 
inference also. To explain this difference. A Frenchman 
makes a flying visit to the United States and then goes home 
to write a book in which he recounts his observations upon 
the character of the American people. But the ' observations ' 
he recounts involve at least three successive sets of infer- 
ences. What he has really observed is a specific set of words 
and acts on the part of this, that, and the other specific indi- 

343 



344 ■ OBSERVATION AND MEMORY. 

vidual. His first inference is that by these words the indi- 
viduals in question intended to convey certain specific ideas, 
and that in the acts they were guided by certain specific pur- 
poses; but he may have wholly misunderstood them both. His 
second inference is that people wishing to convey such ideas or 
acting for such purposes must have such and such character- 
istic conceptions and feelings ; but again he may be mistaken. 
His third inference is that what is characteristic of this score 
or more of individuals whom he happens to have met is char- 
acteristic also of the seventy-six millions whom he has not. 
Once more he maybe wrong. Yet he calls it all observation. 

So with scientists. Their inferences are more careful; but 
still they often use the word Observation to include them. 
Astronomers, for example, may speak of the observed course 
of such and such a comet, when they have only observed a 
few of its positions and have calculated all the rest. Indeed 
in the strictest sense of the word they can hardly be said to 
have observed even a single position. They have perceived 
a speck of light at a certain apparent position in the field of 
a telescope; at about the same time they pressed an electric 
key connected with a clock ; and they have after w^ards read 
off certain figures from various parts of the telescope and its 
attachments. That is all. The position of the comet even 
at one moment is obtained from these data and others like 
them by elaborate calculations. Thus the word ^ observation ' 
is used in science as well as in common life in a very loose 
sense that is likely to deceive because it seems to imply a 
closer contact with immediate experience than it really does. 

Even when we realize all this and do not regard anything 
as an Observation except a direct perception we are not yet 
free from inference. Perceptions are not bare sensations. 
They are sensations interpreted, and the interpretation, how- 
ever rapid and involuntary, is an inference, and may be 
wrong. I see my brother across the road, but when I cross 
to speak to Ifim it turns out to be soirie one else ; I /lear some 
one say ' Be honorable ', but he really said * It's in an enve- 



CREDULITY. 345 

lope ', and so on. These are what psychologists call Illusions. 
Then again we have Hallucinations, when the interpreted 
sensation itself arises wholly from within. I hear my name 
called, see a flash of light, or feel a drop of rain or the crawl- 
ing of ants, when there is nothing there at all. But because 
I say * There is ' a sound, a light, or an insect, instead of 
merely saying ^ I have ' such and such a feeling, or that such 
and such a feeling exists, I am drawing an inference once 
more, and once more it is or may be wrong. The only way 
to avoid all chance of Illusions and Hallucinations is not to 
interpret any sensation. But a live person cannot do this ; 
and if he could and did, he would die. 

' Thus the paradox : induction sets out to base its inferences 
upon the observation of facts, but the observation is itself a 
matter of inference. What then shall we do : reduce the 
element of inference in our observations to the very minimum 
mentally possible, or let it reach a maximum ? AVhat we 
really do in most cases is to infer without scruple until some- 
thing makes us suspect that we have been deceived or that 
we are dealing with a class of facts in which we are likely to 
be deceived; and then, if it is not too late, we turn back and 
examine the phenomena more carefully and critically. No 
one ever thinks of distrusting his ' senses ' so much when he 
is watching a farmer or a carpenter at work as when he is 
watching a conjurer or a ^medium'. In the one case we 
include a great many spontaneous inferences in our ' ob- 
servations ' and say that we saw him do thus and so ; in the 
other case we only say that he seemed to. What we do natu- 
rally in this respect is perfectly logical; for no apparent per- 
ception can be tested except by the surrounding conditions 
as we know them. 

All the difference between the absurd credulity or incredu- 
lity of ignorant peasants and the reasonable judgment of the 
educated depends upon the different extent of 
their knowledge about phenomena like those in 
question or the wider world in which they occur. A scientist 



346 OBSERVATION AND MEMORY. 

never thinks of doubting the existence of other men, and 
thus when he ^sees' a colleague in the room with him 
he believes that the colleague is there. An unsophisticated 
peasant never thinks of doubting the existence of ghosts, and 
so when he ' sees ' a ghost in the room with him he believes 
that it is there. Logically the scientist and the peasant are 
in precisely the same position, and unless we are willing to 
say that the scientist should not be so credulous when he 
believes that he sees something, we have no right to say it of 
the peasant. Incredulity in general is no better than credu- 
lity. The scientist w^ould probably distrust his ' observa- 
tion ' of the ghost, but he does not distrust his observation in 
general. Indeed he distrusts his ' observation ' of the ghost 
only because he trusts his other observations and the infer- 
ences he has drawn from them enough to believe that ghosts 
probably do not exist. Thus in observation, as in every- 
thing else, general faith precedes and has a logical right to 
precede specific doubt. The doubt does not come sponta- 
neously or for its own sake, but it is forced upon us by our 
faith in our other observations and the larger system of 
things which they seem to have revealed. 

If the field of our observations is a new one and we cannot 
tell where it is that the spontaneous inferences which we 
naturally include in our 'observations' are most likely to be 
wrong, the only thing to do is to go ahead bravely yet 
cautiously, placing provisional confidence in our observations 
everywhere, yet always ready to turn back and re-examine 
any point more carefully. The scientist cannot avoid blun- 
ders ; for he sees and hears as other men do, and he drawls 
all their spontaneous inferences j but unlike them he knows 
how much of what he seems to see and hear is really infer- 
ence, and how likely it therefore is that some of his ' obser- 
vations ' are erroneous. Consequently he generally takes 
pains to verify his ol:>servations before he announces them, 
he states them modestly w^hen he does, he expects others to 
verify them for themselves before accepting them, and he is 



unprilJudiced observp:rs. 347 

willing to be corrected when lie has made a mistake. In all 

of which respects he is very different from most of tliose who 

have not received his training. 

Since what we ' observe ' and the faith we put in it depend 

upon what we already believe, it is perfectly evident that 

a wrong belief to begin with will lead to wrong 

' observations ', so that when we are once started Errors 

^ cumulative. 

on the wrong track we keep going further and 

further, and generally find ' sufficient proofs ' for our false 

convictions. 

Trifles light as air 

Are to the jealous confirmations strong 

As proofs of holy writ. 

We pile proof upon proof until at last we stumble across 
some fact so obvious that we cannot ignore or distort it, or 
until we discover that the general conception of things that 
led to so many bad ^observations' is inconsistent with some 
other general conception just as Avell 'established'. Then 
comes the doubt, the true testing of the ^observations', and 
the better general standpoint. The only point in favor of 
the scientist as contrasted with other people isthat he is on 
the watch for such inconsistencies, and therefore corrects his 
blunders of theory and observation sooner. 

This danger of ' observing ' what we expect to observe 
and ignoring what we do not is inevitable. Often we wish 
to submit a fact to an unprejudiced observer. If we mean by 
an ^unprejudiced' observer one who has abso- 
lutely no convictions that can possibly affect his Jibserver^s?^^ 
observations, then the only unprejudiced ob- 
servers in the world are newly born babies who do not even 
believe that there are things and people. But their freedom 
from prejudice makes it impossible for them to ^ observe ' 
anything at all. When we demand the testimony of an ^ un- 
prejudiced observer ' the most that we can really wish is that 
the observer in question shall have no more personal interest 
in one side of the question at issue than in the other, that he 



34^ OBSERVATION AND MEMORY. 

shall have conceived of both sides as distinctly as possible, 
and that he shall then have made his observations dispas- 
sionately, calmly, and deliberately for the sake of deciding 
as fairly as possible between the two sides. We do not ask 
that his mind shall be free from all preliminary convictions, 
but only from those special convictions the truth of which is 
disputed by one side or the other. He is not, and cannot 
be, without prejudice in general, but only without prejudice 
on the questions involved in this particular dispute. For the 
rest, we must expect him to take something for granted. 
Hence if the question changes after the observations are 
made and now the dispute turns upon some point that our 
unprejudiced witness never seriously questioned, his testi- 
mony is no longer of any special value. And so, in general, 
an observation made for the sake of settling one question has 
very little value for the settling of another. When the ques- 
tion is changed the observations should be repeated. 

Errors of observation are divided by logicians into those 
of Mal-Observation, where we perceive things wrongly, as 
Two classes ^^^ J'^^^^ been explained, and those of Non-Obser- 
of errors. vation, w^here we fail to perceive or take account 
of certain important facts at all. Here are some examples 
of the latter. 

'^Most of the books do not give us a psychology, but 
rather a eulogy^ of animals. They have all been about ani- 
mal intelligence, never about animal siupidity. . , . Human 
folk are as a matter of fact eager to find intelligence in ani- 
mals. They like to. And when the aniinal observed is a 
pet belonging to them or to their friends, or when the story 
is one that has been told as a story to entertain, further com- 
plications are introduced. Nor is this all. Besides com- 
monly misstating what facts they report, they report only 
such facts as show the animal at his best. Dogs get lost 
hundreds of times and no one ever notices it or sends an 
account of it to a scientific magazine. But let one find his 
way from Brooklyn to Yonkers and the fact immediately 



TWO CLASSES OF ERRORS. 349 

becomes a circulating anecdote. Thousands of cats on thou- 
sands of occasions sit helplessly yowling, and no one takes 
thought of it or writes to his friend, the professor; but let 
one cat claw at the knob of a door, supposedly as a signal to 
be let out, and straightway this cat becomes the representa- 
tive of the cat-mind in all the books. The unconscious dis- 
tortion of the facts is almost harm-less compared to the un- 
conscious neglect of an animal's mental life until it verges on 
the unusual and marvellous." * 

Again, during a thunder-storm a timid woman often tries to 
justify her fears by recounting all the cases she can remember 
of persons who were struck or nearly struck by lightning in 
previous storms, and forgets the thousands who lived through 
them unscathed. Many a man buys a ticket for a lottery 
because he thinks his ' chances ought to be as good ' as those 
of some acquaintance who once won a prize, but forgets that 
they are also as bad as those of unnamed hundreds who in- 
vested but never won. " Bacon quotes the case of the scep- 
tic in the temple of Poseidon, who, when shown the offerings 
of those who had made vows in danger and been delivered, 
and asked whether he did not now acknowledge the power of 
the god, replied : ' But where are they who made vows and 
yet perished ' ? This man answered rightly, says Bacon. In 
dreams, omens, retributions, and such like, we are apt to 
remember when they come true and to forget the cases when 
they fail." t 

Errors of observation are sometimes spoken of as Fallacies. 
This does not mean that it is a fallacy not to see something 
that is there. The fallacy comes in when we infer that it was 
not there because we did not see it. I may not notice the 
number of times that dreams fail to come true, but I commit 
no fallacy unless this makes me infer that they come true 
much oftener in proportion than they really do. In the same 
way it would be rather a straining of language to call an 

•^ E. L. Thorndike, ''Animal Intelligence", pp. 3-5. Macmillan* 
■j- Minto's "Logic", p. 24, 



3SO OBSERVATION AND MEMORY. 

erroneous observation a fallacy. The fallacy or blunder in 
reasoning comes in when we do not make proper allowance 
for the possibility of such errors, and insist that something 
must be true because ' we saw it ' . 

When an observation is not fully recorded at the time of 
making, the danger of error is twofold ; for we are quite as 
likely to be wrong in our memory of the observa- 
its^angers^.^ ^^^^ ^^ ^^ ^^^ observation itself. The longer the 
time between the observation and the recollection 
the greater in general is the danger of error. ^^ Col. Nicolay 
is reported to have said that he and Mr. Hay received very 
little aid from contemporary memories in writing their his- 
tory of Abraham Lincoln, and that they came to the con- 
clusion that mere memory unassisted by documentary evidence 
was ^utterly unreliable after a lapse of fifteen years '." >1^ 

The dangers in the case of Memory are like those in the 
case of observation. We may forget, and if we insist un- 
reasonably that we never had a certain experience because 
we cannot remember it, we commit precisely the same kind of 
blunder as when we insist unduly that a thing was not present 
because we did not observe it. 

When we do ^ remember ' we are more likely than not to 
get some of the details wrong, and sometimes we take ^ recol- 
lections ' for true when they are really complete inventions. 
Errors of the first kind correspond to illusions in perception; 
those of the second kind to hallucinations. 

In memory as in perception we constantly tend to find 
what we think we ought to find. When we tell a story of 
some past conduct of our own we almost inevitably 
rememYer. ^^^^^^ it more logical and coherent than it really 
was. We had the motives that we ought to have 
had, we said the clever things that we ought to have said, 
and the mere blind impulses and incoherent acts and mean- 
ingless speeches are forgotten altogether or twisted into 

^ W. H, Burnham, <' Memory", Am. Jour, of Psychology, II, 235. 



WHAT WE REMEMBER. 35 r 

shape. ^ When things are simply incoherent and meaningless 
we cannot remember them any more than we can observe 
them. We may remember that there was something incoher- 
ent, but we cannot remember or describe it without giving it 
a certain coherence, even if it be a coherence of absurdity. 
When someone makes a meaningless speech we either give it 
a reasonable meaning, forget it altogether, or make it a kind 
of monstrosity far worse than it really was. If it does not 
make a definite impression of some kind or other, we forget it. 
If it does, we fill in all the details to fit our notion of the whole. 
It is the same way in our recollection of an argument or a 
quarrel. We were right and our opponent was wrong ; and 
we remember our good sayings or acts and his bad ones 
because they fit in with the impression of our rightness, 
and forget our bad sayings or acts and his good ones because 
they do not fit in with this impression and are therefore in a 
sense purely irrelevant. Or it may be that we are impressed 
with the wrongness of our case, and then we go to the other 
extreme and remember our own bad sayings and acts and his 
good ones and forget our own good and his bad. In either 

* "Mere illusions of memory suggested by present impressions are 
common in normal life. As we apperceive any object or event through 
the media of the feelings and ideas in consciousness at the moment, and 
thus no two of us apperceive the same thing in the same way, so in rec- 
ollection each apperceives the past from the standpoint of his present 
state of consciousness, and the latter bears its part in determining what 
the resulting recollections shall be. We remember only main features 
of an event anyway, and the imagination fills in the gaps. Thus re- 
membrance is never a true reproduction of reality. It is always more 
or less an illusion. At best it is an approximation to the truth. How 
near an approximation depends largely upon the apperceptive mood of 
the moment." (W. H. Burnham, "Memory", Am. Jour, of Psychol- 
ogy, II, 449-50-) 

Consistency according to the laws of nature is the only test of truth ; 
but consistency in conduct is consistency according to a purpose, and 
this is only an ideal. When a person tells a story that makes all his 
acts or all the acts of his hero rational and consistent, we can be quite 
sure that it is not true. 



352 OBSERVATION AND MEMORY. 

case the recollection is distorted by the almost inevitable ten- 
dency to remember things as coherent wholes capable of brief 
and definite description and congruent with the emotion of 
the moment. 

As memory distorts the inner content of an experience 
itself, so it may easily distort its relation to other experiences ; 
and then we get the dates and places wrong. We feel that 
experience A must have taken place in connection with B, 
possibly because that is the logical order, possibly because 
we have often thought of them together ; and yet as a matter 
of fact they may have been miles or months apart. 

Serious consequences often result from this erroneous 
^ recollection ' of the connections between experiences and 
Honest ^^^ corresponding forgetfulness of their real con- 

^^^^* nections. If we remember a dream or a fancy 

with such vividness that it has the feeling of reality and do 
not remember the outv/ard relations that would clearly dis- 
tinguish it as a dream or fancy, it will seem to us that what 
we are remembering is not fancy but fact, and we easily fill 
in the connections that facts like those ' remembered ' ought 
to have. Thus there are people who lie, and lie habitually, 
with the very best faith. The only possible remedy for 
this unconscious lying is to distrust one's own memory and 
deliberately test or verify one's 'recollections' in every case 
of importance ; and if one does not wish to be deceived by 
others, he must distrust theirs too. Lawyers are proverbially 
unsatisfactory witnesses, simply because they know how 
uncertain memory is, and only say ' I think so ' , when others 
far less accurate and careful say ^ I know ' ; and of course the 
confident assertions of the man who ' knows ' carry far more 
weight with the ordinary juryman than the hesitating beliefs 
of the one who only * thinks so ', 

'' The medico-legal aspect of this subject is of the most 
practical importance. The more common forms of param- 
nesia [or false memory] . . . show that it is not impossible 
^.0 manufacture testimony. A member of the bar tells me 



HONEST LIES. 353 

that this is actually done in some cases, the method employed 
being somewhat as follows : The witness is a person of 
deficient memory. It is desirable that he should testify to the 
occurrence of a certain event. The lawyer asks the witness 
if he remembers this event. The reply is, No ; and nothing 
more is said. But the idea of the event has been suggested 
to the mind of the witness. In a few weeks the lawyer re- 
peats the same question, and again receives a negative answer. 
But after a few similar experiments the witness becomes un- 
certain whether he remembers the event in question or 
not. He begins to think that he does. The images of 
the imagination suggested by the lawyer's questions loom 
up vaguely in the mind, the memory is confused, and 
in a few months the lawyer, if skilful, may develop a 
pseudo-reminiscence so strong that the witness will give 
the desired testimony with complete sincerity. Of course 
this cannot succeed with persons of strong memory and 
critical judgment, but with children and aged people it may 
not be difficult. . . . 

*^ Nothing, as Motet says, is more effective than a child's 
story of the details of a crime of which he pretends to have 
been a witness or a victim. The child's naivete adds to the 
interest and elicits confidence. His hearers urge him on by 
their sympathy. Parents, friends, and neighbors accept the 
account, true or false. They suggest new details and fill up 
the gaps in the story. The child's uncritical mind assimi- 
lates these details, repeats the story without variation, and 
makes his accusation before the magistrate with an apparent 
accuracy that is most telling. . . . 

^^The uncertainty of human testimony was notably illus- 
trated a few years ago in the case of the Bell Telephone Co. 
vs. the People's Telephone Co. The chief point at issue 
was whether Daniel Drawbaugh had a telephone in his shop 
prior to 1876. Several hundred witnesses gave testimony 
bearing directly or indirectly upon this point. The honesty 
of most of the witnesses seems to have been admitted, yet 



354 OBSERVATION AND MEMORY. 

evidence offered by one side was generally refuted by testi- 
mony from the other. The Supreme Court divided upon the 
case, and the seven thousand printed pages of evidence in the 
suit seem rather to prove the fallibiUty of human testimony 
than anything else. See article on Daniel Drawbaugh, by 
H. C. Merwin, Aikmiic Monthly, Sept., 1888." * 

Since memory is always unreliable, almost the first thing 
for one who is doing scientific work of any sort, no matter 
how humble, to learn is the imj^ortance of keepiiig 
common- full and clear records of every detail of his experi- 
ments or observations that may have the slightest 
bearing on the question at issue. If a detail is to be pre- 
served at all, it must be taken down at once ; it is usually 
almost as easy to take down a point of doubtful value as to 
neglect it, and the best and most accurate of experimenters 
are only too liable to find their work less valuable than it 
might otherwise have been because there was some small 
detail of which they did not make a note. Most beginners 
need to be warned, too, not to keep notes on loose scraps of 
paper, not to use unfamiliar abbreviations without writing 
down their meaning, and to make their writing very legible. 
If they themselves are to be sure of its meaning, the record 
should be so clear and unambiguous that it could be easily 
understood by any one. In other words, it should be a true 
record, and not a mere series of suggestions for the memory. 
It is important, too, to number the pages (unless the record 
is in a book) and to leave plenty of blank space on each of 
them. There is a strong tendency to get things crowded 
some time or other before the results are finally computed, 
and a crowded record is very confusing. Finally, the notes 
should be indexed and put away in such order that they can 
be found at a moment's notice for years afterwards. To 
observe these simple precautions is to save much time and 
annoyance for everybody concerned ; and what is said here 

* W. H. Burnham, loc. cit. 



RESULTING COMiMOxXri.AC IS. 355 

about scientific work is just as true, mutaiis inutandis, of a 
farmer trying to remember what his fields have done each 
year, or of business, school-teaching, housekeeping, or any- 
thing else where it is worth while to remember transactions 
accurately. 



CHAPTER XXXIV. 

THE DISCOVERY OF PAST AND FUTURE EVENTS IN 

GENERAL. 

When we wish to ascertain some specific fact that we have 
not been able to observe for ourselves there are only two ways 
of doing it. One is to depend upon the testimony of others ; 
and the other is to draw an inference from what we know of 
the general laws of nature and the specific facts that we or 
others have observed. The latter method can be described 
very briefly, and so we shall speak of it first. This is the 
method used in tracing the history of the solar system from, 
or rather back to, the vapor and the star- dust from which the 
planets were made and in prophesying the condition of cold 
and darkness and lifelessness to which they may be destined. 
It is the method pursued by geology m tracing the changes 
which have taken place on the earth's crust and prophesying 
those which will take place. And it is the method pursued 
by evolutionary biology in tracing the history of life in the 
world as it has developed from one form to another. In all 
these sciences the starting-point is the present, and the ques- 
tion is always this : Granting the truth of the general laws 
assumed or ascertained by various sciences, what is the only 
concrete state of affairs that could have preceded the one 
which we observe to exist at the present, and what is the 
only concrete state of affairs that can succeed it ? 

The first thing to notice about this method is that we 

356 



THE STARTING-POINT, 357 

always start from the present. In telling about history of 
any sort we may often begin ' at the beginning '. The start - 
In investigating it we never can. Moreover, if ing-point. 
we are mistaken about some of the general laws or if we are 
not quite accurate about some of the concrete facts with 
which we start, the consequences of our error will affect all 
our history and all our prophecy ; and since there is a 
chance of overlooking some essential fact or making some 
miscalculation at each stage of our regress into the past or 
progress into the future, the chances are that the farther we 
go the less accurate our account of things can be. The pos- 
sibility of such accumulation of errors will always make a defi- 
nite and detailed description of the world more doubtful the 
farther the described state of affairs is removed from the 
present data with which we have to start. But indeed what 
we know about the laws of nature and present concrete con- 
ditions is so slight in comparison with what we do not know, 
and even those things that we do know are so enormously 
complex, that no one really attempts to work out the prob- 
lem in all its details, and the most that any scientist attempts 
to tell about either the distant past or the distant future is 
the broad outlines of things, which would remain substantially 
the same no matter what were true about anyone of countless 
smaller details. A geologist can tell with perfect confidence 
that where there is now a certain group of hills there was 
once a fairly level plateau, and he can tell that the change 
from one to the other was due in the main to the action of 
water running down to the valley below, but he would never 
attempt to tell the exact location of every stream or the 
amount of earth that one of them carried down on some par- 
ticular day ten thousand years ago. 

Even what a geologist does tell about the past and the 
future is not based upon the most ultimate laws of matter 
known. If it were, he would have deduced the history of 
the world from the known laws of chemistry and molecular 
physics ; and such deduction is impossible because the situ- 



358 THE DISCOVERY OF PAST AND FUTURE EVENTS. 

ations that these sciences deal with are exceedingly simple, and 
from the relations that are found to exist in these simple sit- 
uations no one could possibly calculate what would happen 
under the vastly more complex conditions that are dealt with 
m geology. The geologist starts rather with ' empirical 
laws ' which are much less precise ('^o far as particular mole- 
cules are concerned) than the laws of molecular ph)'sics, but 
which give a much better idea of what happens when things 
are arranged as he supposes them to be in the large. He sees, 
for example, that streams actually do wear away earth and 
rock from their beds and carry the debris away, and he de- 
termines by actual measurement the amount of earth of a 
given kind that a stream of a given size and swiftness carries 
off in a given length of time ; and then he applies the 
'empirical law' which he derives from such measurements 
directly to the problem in hand. He knows, of course, 
that the facts m the case are consistent with molecular physics, 
but he knows also that his data are much too crude and 
complex to be dealt with by that science ; and so he works 
away with his ' empirical laws ' in comparative oblivion of it. 
Almost all of our history of the world and our prophecy of 
its future is based upon such ' empirical laws ' as these, 
derived from a view of things in the large; and of course 
any history or prophecy which is based altogether upon such 
broad rough laws cannot attempt to describe small details. 

Another thing to notice about scientific history and proph- 
ecy IS that there is nothing in the laws and concrete facts 

upon which they are based to tell the scientist 
The limit. , , , , i i ^ i . 

when the whole world-process began or when it 

will come to an end. For all we know or ever could know, 
God may annihilate the whole world to-morrow ; but our 
prophecy based on laws and concrete facts of the present looks 
forward without limit towards a whole eternity. In the same 
way we trace what we suppose to be the broad outlines of his- 
tory further and further into the past, and we never reach and 
never can reach a point at which we can say : Here everything 



'MONUMENTS/ 359 

must have begun. If the world ever was made and wound up 
like a watch, whether five thousand years ago, as theologians 
used to suppose, or twenty-four hours ago, we can never see 
anything on the face of it to indicate when that took place. 
All we can say is that if this world-watch really was going six 
thousand years ago as it is going now, then at precisely that 
time the hands were in such and such a position. 

It seems much easier to believe that the world started five 
thousand or five billion years ago than twenty-four hours ago, 
merely because our whole conception of so distant a past is 
vaguer. But if it started five thousand years ago, it started 
with fossils in the rocks and all the other absolutely definite 
conditions that must have preceded the present and that lead 
scientists to trace its history beyond the five thousand years 
of its actual existence. And if it started five billion years ago, 
every detail must have been just as definite; however hazy 
our idea of it may be. It might just as well have been cre- 
ated twenty-four hours ago with mines half empty and cities" 
all built and ships in the harbors, and adult human beings 
busy at their work, with brains so fashioned that they look 
back towards an imaginary past and believe they remember 
it. Thus, starting from the present as science does and must, 
and assuming as it does that things acted in the past and will 
act in the future according to the same laws that we find now, 
it is quite impossible for us to find any point at which the 
world-process must have begun or must come to an end, even 
if there really was such a -beginning and really will be such an 
end. 

One might think that the uncertainty due to the frag- 
mentary nature of our knowledge and this possible accumula- 
tion of errors should affect our knowledge of the . jyionu- 
past quite as much as our knowledge of the future ; i^ients.' 
but as a matter of fact it does not. We know a great deal 
more about the past ; and the reason is that many conditions, 
when they are once produced, remain practically unaltered 
for a great many years. No geologist can tell whether the 



360 THE DISCOVERY OF PAST AND FUTURE EVENTS. 

place where I am now writing will ever be covered with 
water or not ; but from the layer of gravel beneath the sur- 
face of the ground I can infer with reasonable certainty that 
once it was. No one can tell whether Vesuvius will ever de- 
stroy a city again, but from the buried remains of Pompeii 
and from written records we can *infer that once it did. This 
is merely because we have reason to believe that such things 
as beds of gravel, the stones of buried cities and forgotten 
documents remain comparatively unchanged for years or cen- 
turies. Thus when we find such things they take us at one 
leap beyond all the intervening years, and each of them 
shows us one fragment of the past as it existed at the time. 

Accordingly, if we are right in assuming that such relics of 
the past have remained unaltered in any given respect, and 
if we have any means of finding out their age, we can use 
each one of them as a starting-point in the construction of 
the past, or at least as something fixed by which to test our 
inferences about it. In such cases we might almost say that 
we really do start with the past. This is why we can tell 
more about some things in the past than in the future ; why 
there is such a thing as serious history where there is no 
corresponding prophecy. 

It is because there are such absolutely or relatively perma- 
nent ^ monuments ' of the past as these that it is possible for 
us to distinguish between relatively dij^ect evidence concern- 
ing past events and indirect. The most direct evidence con- 
cerning any event is, of course, the present and personal 
perception of the event itself. This is something independ- 
ent of ' monuments ' of any sort, but if the event is past, this 
evidence is unattainable. The most direct evidence then 
possible is the perception of something which we can assume 
to be a direct effect of the event, and after that the supposed 
effects of effects of the event or the supposed effects of some- 
thing that would have caused the event ; until the chain is as 
long or crooked as you please. The most direct evidence of 
the destruction of Pompeii by a volcanic eruption would be 



CIRCUMSTANTIAL EVIDENCE. 36 1 

the perception of the event itself. The most direct evidence 
possible for us is the personal perception first of the unbroken 
lava and then of the houses being dug out from beneath it. 
Photographs of such lava-beds and houses give less direct 
evidence, and the tales of persons who claim to have seen 
such photographs less direct still. 

It is hardly necessary to add that the most reliable evi- 
dence about past events is afforded by monuments which we 
know to have undergone the least possible change, and which 
are connected with the events under investigation by the 
shortest and surest series of causal relations. The value of 
written records as monuments of the past wnll be spoken of 
in the next chapter. 

One hears a great deal in discussions of criminal trials 
about circumstantial evidence. Evidence is called circum- 
stantial w^hen the witnesses have not observed, Circum- 
and therefore cannot tell about, the very fact at evidence. 
issue (^.^., A murdering B), but can and do tell about 
various other facts so connected with the fact at issue by the 
law of causation that from them the jury can infer what that 
fact really was. Thus ' circumstantial evidence ' is only the 
common name for indirect evidence of the sort that may be 
given in a court of law. If A and B were heard talking 
loudly as though they were in a violent dispute and if A was 
afterwards seen leaving the house covered with blood, wdiile 
B was found stabbed to the heart with A's knife, there would 
be good circumstantial evidence that A had killed him, and 
he might very well be convicted and hanged for a crime that 
no one had seen him commit. 

Circumstantial evidence is conclusive only if a supposed state 
of affairs is the only one that will fit in with the ascertained 
facts according to the general laws of nature. In a simple 
case of astronomy or chemistry a conclusion of this sort can 
be drawn with practical certainty ; but with human affairs 
the case is somewhat different ; for human life and the con- 
ditions that determine it are so exceedingly complex that it 



362 THE DISCOVERY OF PAST AND FUTURE EVENTS. 

is very rarely possible to say with anything like certainty : 
This supposed state of affairs and this alone is consistent 
with all the established facts. In the case given, for example, 
it is quite possible that B was seized with a sudden mania 
during which he first picked a quarrel with A and then seized 
A's knife and stabbed himself, while the blood on A was due 
to his efforts to prevent B from doing the mad deed. Or it 
might be that A and B were not quarrelling with each other 
but with some third person, who had afterwards picked up 
the knife, committed the murder and then made his escape. 
Or the real truth of the matter might be something entirely 
different that nobody happens to think of at all. A person 
convicted of some crime on circumstantial evidence is thus 
often convicted on a degree of probability which falls con- 
considerably short of practical certainty ; which means, of 
course,* that amongst a large number of such cases there are 
a few in w^hich the person convicted and punished is really 
innocent. This accounts for the general feeling of uneasiness 
or dissatisfaction when a trial of vital importance is decided 
altogether upon circumstantal evidence. But we must re- 
member that the uncertainty of a conclusion based upon such 
evidence is due to the complexity of the situation dealt with 
and our ignorance of many of its details, not to a defect in 
the general principle ; for the principle is that involved in all 
indirect evidence, and it is the only one in virtue of which 
w^e can gain any knowledge whatever of either the past or 
the future. 

* See p. 334. 



CHAPTER XXXV. 

TESTIMONY. 

Amongst the most important monuments of past events are 
the impressions made by them on the minds of persons who 
were present at the time. From these impres- itsimpor- 
sions, if we can find out w^hat they are, we can often ^^^^' 
judge the nature of the events that made them. Yet the im- 
pressions in the minds of others can never be observed directly, 
but only inferred from what they say and do. Hence there is 
always a double inference : from what a witness says to his 
thoughts, and from his thoughts to the events that caused them. 
The necessity for this double inference often makes the correct 
estimation of testimony very difficult ; and yet in all matters 
of history — whether they be the events of last w^eek told in a 
police court or the events of two hundred years ago set forth 
in a formal treatise — its proper estimation is most important. 
If we estimate it wrongly we are bound to reach false conclu- 
sions ; and if we ignore it altogether we can hardly reach any 
conclusions at all, for apart from the memories of men and 
what they have written we have very few unaltered monu- 
ments of the past life of individuals, and our human environ- 
ment is so complex and our knowledge of human nature so 
slight that an investigator who tried to find out about the past 
deeds of anybody else merely by going back step by step from 
his own personal experiences w^ould hardly get started before 
he had to stop. 

Even if there were plenty of other evidence, reliable testi- 

363 



364 TESTIMONY. 

mony would still have a great and very unique value. It sets 
the whole scene before us, presumably as we our- 

value and selves would have seen it if we had been there, 
dans'Ci'* 

with the important details accented and the mean- 
ingless trivialities omitted or properly subordinated ; and thus 
without much trouble on our part it gives us a warm, human, 
unified account of the whole matter at a single sitting, in- 
stead of leaving us coldly and laboriously to construct it all 
bit by bit from various remnants of impersonal evidence that 
give the trivial and the important all together and leave us to 
find out what are the points of essential human interest for 
ourselves. In this way testimony enables us to reap the fruits 
of some one else's perceptions and inferences. But this has 
its dangers, for it tends to put us at his mercy if he chooses 
(as mere inanimate relics of the past cannot) to deceive us, 
and to make us share his errors if his perceptions, inferences, 
or memories were wrong. How then can we be sure in any 
particular case that there is no mistake and no falsehood, and 
that the words of the witness have therefore given us anything 
like the idea of the matter in question that we should have 
had if we had observed it for ourselves ; and if we cannot 
be sure of this, how can we make use of testimony at all? 

It is easier to answer this question now than it would have 
been while we were discussing the inductive methods by 
which we learn the laws of nature ; for throughout the whole 
discussion we simply took for granted that when people are 
working together for a common end they trust each other, and 
have a logical right to do so. Now that the question is raised 
we shall find that in every specific case the answer depends 
upon our knowledge of these very laws that we learned 
largely through the aid of our spontaneous faith in one another. 

The weighing of testimony involves some departure from 
Accepting, ^^^^ attitude that we take most naturally and spon- 
and we^lii- taneously towards the stories that are told to us. 
i^8^- Our first natural attitude towards testimony is 

one of trust ; not because we have reasoned that it is trust- 



ACCEPTING, REJECTING, AND WEIGHING. 365 

worthy, but merely because we cannot help it. If it had not 
always been natural to accept the statements of those about us 
as substantially true, we should probably not be alive now to 
discuss the matter; for the telling of the truth on the one hand 
and confidence in the story told on the other are very impor- 
tant means for the preservation of the race. Each of us is born 
into a larger or smaller community with common interests : 
a common living to gain, common diseases to avoid, and 
common enemies to overcome. We can attain these common 
aims only by co-operation, and we cannot co-operate intel- 
ligently unless we all have approximately the same ideas. In 
warfare the chief must rely upon the scouts for knowledge of 
the position and numbers of the enemy, and, on peril of its 
existence, the whole tribe must act upon that knowledge as 
the chief commands. A sceptic who refused to believe and 
obey would be likely to sacrifice his own life and perhaps 
that of the tribe as well to his rebellious incredulity ; and so 
likewise with the chase, sanitation, and other relations of life. 
Since we are all fitted for this life in common it is almost 
as natural for us to share the ideas of our friends as to share 
their interests, and to accept the beliefs of those in authority 
as to obey their commands. Indeed it is no accident that 
the words Yes and No, which are used to express obedience 
or consent and their reverse, are also used to express intel- 
lectual assent and dissent, and that such words as Ally, Op- 
ponent, Our Side, Their Side, Attack, Rescue, Beaten, Vic- 
tor, are used as much with reference to a ' conflict ' about 
some matter of opinion as to any other, however deadly.^ 

* This need for a community of thought within the tribe as well as of 
action is expressed in many ways. In the heat of a military or political 
campaign a man who says that his country or his party is in the wrong 
is branded as a traitor. In religion the demand for uniformity of belief 
has shown itself in state churches with their old-time persecution of 
heretics and the modern prosecutions for heresy, in the maintenance of 
our various Protestant sects on a community of creeds rather than of 
aspirations, and in the feeling we often find that even though a belief be 
true it is wrong to accept it if the Church says otherwise. Even social 



366 TESTIMONY. 

Along with this tendency to accept without question the 
statements of those whom we love and honor there soon grows 
up the tendency to reject the statements (whether we believe 
them to be sincere or not) of those whom we hate or despise. 
' The truth for friends and lies for enemies. ' This is a good 
rule of tribal policy and one so often followed that even in 
modern warfare, and often, too, in modern diplomacy, we ex- 
pect the enemy to deceive us if he can. Even when we are 
sure that we know the real beliefs and institutions of another 
tribe, we feel that they cannot be accepted without disloyalty 
to our own. If any one is a foreigner or an ' Outlander ' , that 
is enough to make his language, his clothing, his customs, and 
his religion all ' outlandish '. We do not weigh his opinions 
any more than we consider his interests ; we simply reject 
them with contempt. In the same way with private individuals 
within the family, the tribe, the nation, or the church, if th^y 
antagonize us it is almost a point of honor with us to dis- 
prove, or at least to disbelieve, everything they say. Thus 
we tend to accept the statements and the real beliefs of our 
friends and to reject those of our enemies; but not to weigh 
either the one or the other. 

This rough instinctive way of accepting and rejecting 
testimony is good enough in the main for children and for 
the plain men and wom.en who are content or compelled all 
their life to follow the lead of others, if the leaders are already 
given. But it is not sufficient when there is a conflict of 
authorities and one has to choose his leader. It is not suf- 
ficient either when a person wishes to go without a leader 
and perhaps to become a leader himself; that is to say, when 
he differentiates himself from the rest of the set, whether it 

classes tend to have their own characteristic beliefs, and one rejects 
those of another without argument as visionary, aristocratic, or vulgar. 
Science itself is not free from the same influence, for there are different 
< schools ' of philosophy and medicine as well as of theology, and an 
odiu??i niedicum as well as an odiiwi theologicum. The whole tendency 
can be summed up in the common use of the phrase Vox populi vox Dei, 



EXPERT EVIDENCE. CAUTION. 367 

be family, tribe, nation, church, or social clique, and feels 
that he has interests which the others do not share, or feels 
that he knows more than the rest or observes more carefully 
or has better natural judgment or a better standpoint from 
which to judge. A person in either of these situations who 
has testimony to deal with and who wishes to act rationally 
must try to settle his problem for himself in the light of 
what he already knows about the world and its laws. 

In the first situation he must weigh as best he can the 
merits of the rival authorities. That is to say, he must try to 
find out what causes would naturally make a person an author- 
ity on such matters and then inquire how many of these were 
present in the case of each of the claimants. In the second 
situation, where he is trying to find the truth through testi- 
mony about some matter without the appeal to any authority, 
he must ^ weigh ' the testimony itself. This simply means 
that he must treat all the testimony on the matter as an effect 
and inquire what causes could have produced it. In either 
case he must settle his question by an appeal to the known 
uniformities of Nature ; and if he does not assume that Nature 
is uniform, he cannot settle it rationally at all.^ 

When the question at issue is one about which we cannot 
hope to judge altogether for ourselves because a wholly inde- 
pendent judgment requires technical knowledge 

r T ^ Expert 

of a sort that we do not possess, we must appeal evidence, 
for aid to those who do possess such knowledge ; 
but we must take care to avoid the fallacy known as the 
'Argument from Authority' (^Argiimentiim ad Verecundiani). 
This expression does not mean that every appeal to authority 
is fallacious. The fallacy arises only when, awed perhaps 

* By finding the truth in a case of this sort we mean finding what we 
ourselves should have perceived if we had been present, or what would 
have been perceived by some one else who shares our interests and has at 
least as good natural ability and training. We do not mean finding the 
absolute truth, as God might perceive it ; for very likely that would not 
fit into our general conception of the world at all, 



S6S TESTIMONY. 

by the greatness of a name,* we accept as expert opinion the 
dictum of some one, however great in some other direction, 
who is not an expert on the matter in question. A minister's 
training may fit him to speak with authority about the world 
to come, but not about the vahie of a patent medicine. A 
barber knows how to cut hair, but that gives him no special 
skill in preparing a hair-tonic. A great scientist is not nec- 
essarily an authority on metaphysics ; , a great philosopher 
(such as Kant or Hegel), on the history of philosophy ; a 
great soldier, on politics; or a successful evangelist on 
Church history or Biblical criticism. ^ Practical business 
men ' often speak with scorn of the ^ theorists ' who differ 
from them on economic questions, though the very necessity 
for knowing the details of their own business may keep such 
men from seeing the general relations of all a country's in- 
dustries. A telescopic survey of the world is called for, and 
they claim to speak with authority because they have a 
microscopic knowledge of a corner in a city lot ! 

Similarly a scientist who is great because of his power to 
collect facts may be a poor interpreter of them ; just as a 
skilful census-enumerator might be utterly unable to explain 
a single figure in the returns. 

This IS a fallacy which one can never be sure of avoiding, 
unless he sets out to believe nothing at all. The great thing 
is to select one's experts with proper care and then trust them 

* * ' Even proper names themselves do not seem always spoken w^ith a 
design to bring into our view the ideas of those individuals that are sup- 
posed to be marked by them. For example, when a schoolman tells me 
* Aristotle hath said it ', all I conceive he means by it is to dispose me 
to embrace his opinion with the deference and submission which custom 
has annexed to that name. And this effect is often so instantly pro- 
duced in the minds of those that are accustomed to resign their judg- 
ment to authority of that philosopher, as it is impossible any idea either 
of his person, writings, or reputation should go before. So close and 
immediate a connection may custom establish between the very word 
Aristotle and the motions of assent and reverence in the minds of some 
men/' (Berkeley, '' Principles ", Introduction.) 



EXPERT EVIDENCE. CAUTION. 369 

only where they are strong. When selected the best of them 
will often be found to have marked tendencies in one direc- 
tion or another — "personal equations" — for which due 
allowance must be made. We see best the side of things 
with which we are most familiar and in which we are most 
interested. It is thus natural enough that a physician, for 
example, should fmd nothing but physical disease behind 
some act that a clergyman might attribute altogether to sin. 
Indeed physicists and biologists often tend to ignore such a 
thing as conscious thought altogether or to treat it as a mere 
by-product of bodily life, while idealistic philosophers return 
the compliment by ignoring or denying the existence or the 
influence of the body. So, turning from training to tem- 
perament, a cruel man skilled in statecraft might advocate 
a measure of which a humane man equally skilled might 
wholly disapprove. Then, too, personal interest often affects 
our judgment, not because we wish it to, but because it keeps 
us constantly thinking of our own side of the case, which 
consequently gets well thought out, while the other sides does 
not. In the Southern States, where economic conditions 
made slavery profitable, it was regarded as a divine institu- 
tion ; in the North, where economic conditions had crowded 
it out, it was regarded as diabolical. Such interests are likely 
to affect experts as well as others. 

Three specially flagrant kinds of fallacious arguments from 
authority are what Whately calls the Fallacy of References, 
the appeal to what Minto calls the Abstractly Denominated 
Principle, and what we may call the Appeal to an Imaginary 
Expert. 

The first of these, which, according to Whately, is " par- 
ticularly common in popular theological works'', consists 
in making a great show of scriptural or other authority for 
some particular doctrine by, not quoting, but merely giving 
references to a large number of passages that have some 
bearing or other upon the subject, though few or none 
of them *' distinctly and decidedly" favor the opinion in 



370 TESTIMONY. 

question; ** trusting that nineteen out of twenty readers will 
never take the trouble of turning to the passages, but, taking 
for granted that they afford, each, some degree of confirma- 
tion to what is maintained, will be overawed by seeing every 
assertion supported, as they suppose, by five or six Scripture- 
texts '\ 

In the appeal to the Abstractly Denominated Principle, 
*' A conclusion is declared to be at variance with the princi- 
ples of Political Economy, or contrary to the Doctrine of 
Evolution, or inconsistent with Heredity, or a violation of 
the sacred principle of Freedom of Contract'' (Minto); or 
appeal is made to the Monroe Doctrine or the Rights of 
Man or the Law of Nature or the Nature of God, or anything 
else that is vague, but high-sounding and terrifying. '' It is 
assumed that the hearer is familiar with the principle referred 
to '\ though it may well be that neither hearer nor speaker 
really knows anything about it. The only thing for the 
hearer to do in such a case is to stand his ground and 
frankly confess his ignorance, if he is ignorant, and demand 
an explanation of the principle and of its precise bearing on 
the question at issue. But this often requires great courage. 

As an example of an appeal to an abstractly denominated 
principle we may perhaps take the argument of Cardinal 
Manning against vivisection. It runs somewhat as follows: 
' Truth of Nature must be sought only by methods in 
harmony with the perfection of Nature's God. Mercy is 
one of the perfections of God. Vivisection is not in harmony 
with perfect mercy. Therefore truth must not be sought by 
vivisection.' To all of which Professor Hodge replies: 
'' How the worthy cardinal knows that vivisection is not in 
harmony with God's perfect mercy he nowhere explains." 
{Popular Science Monthly, Sept. 1896.) 

By the appeal to an Imaginary Expert I mean the stating 
of one's own opinions in such a way that they seem to carry 
with them the weight of expert testimony, though really no 
expert is quoted at all. Benjamin Kidd's ''Social Evoh.i- 



INFERRING WITHOUT TRUSTING. 3^/1 

tion ", for example, is full of passages in which the author's 
opinion is backed up by that of an imaginary y^//«r^ expert, 
thus: " Yet nothing can be clearer to the evolutionist when 
he comes to understand the nature of the process in progress 
throughout our history, than that those ideals have been 
and are quite foreign to our civilization" (p. 142). "It 
has been the custom to attribute the success of the Revolu- 
tion to the decay, misrule, and corruption of these classes; 
but history, while recognizing these causes, will probably 
regard them as but incidental. Its calmer verdict must be ", 
etc. " A fuller and franker recognition of the true position 
. . . must apparently be one of the features of the work of 
the future historian who would do justice to the Revolu- 
tion '' (pp. 185-6). "At a future time, when the history 
of the nineteenth century comes to be written with that 
sense of proportion which distance alone can give, it will 
be perceived that", etc. (p. 299; see also pp. 301, 310, 
edition of 1895). 

Kidd IS not the only sinner in this respect. I have just 
run across the following sentences m Harper s Magazine : 
" There were to follow many more desperate encounters. . . . 
But in all probability the careful historian will yet decide that 
in shaping events which, step by step, wrought the downfall 
of the Southern coalition, Fort Donelson stands pre-eminent. 

Leaving this question of how a layman should deal with 
the testimony of real or alleged experts on matters about 
which he cannot pass an independent judgment, let us turn 
again to the principles according to which we should deal 
with testimony as to matters of fact concerning which we are 
not wholly incompetent to judge for ourselves. 

To find the whole truth which lies behind a statement will 
always be impossible for a human being; for that means dis- 
covering and distinguishing between all the 
innumerable causes that may have contributed without 
more or less to produce it. Our knowledge is 
far too slight, our perceptions are far too inaccurate, and 



3?^ TESTIMONY. 

our powers of calculation are far too limited for this. To 
find a part of the truth is a very different matter. We can 
often do this by causal inquiries without raising the question 
of truthfulness — which seems so important when we are 
merely accepting or rejecting statements — at all. 

If a seedy-looking stranger rings your door-bell and says 
that he has not had anything to eat for three days, you need 
not inquire into his truthfulness in order to infer that he 
wants you to give him something and does not expect you 
to hand him over to the police. In the same way, if some 
one wrote a book that is obviously intended to help a certain 
cause, it is evidence — whether he believed what he said or 
not — that at the time he wrote, such a cause existed and at 
least one person thought it important enough to write about. 
If he told a marvellous tale to amuse his readers, we can tell 
that he expected readers and expected them to be amused by 
a tale of that kind. If he is hopelessly prejudiced, we can 
conclude that in his time it was possible for that particular 
kind of prejudice to exist. When he tells about some event 
of which he was a witness he may be both careless and 
untruthful, and yet there is always something that he reveals 
incidentally. An eye-witness may get many of the details 
of a great battle wrong, but he is not likely to discuss the 
way in which the combatants managed their bows and arrows 
and the manoeuvres of the triremes if the battle was really 
fought with Maxim guns and Mauser rifles a hundred miles 
from any navigable water; and it is certain that he will not 
talk of Maxims and Mausers and ironclads if he lived in an 
age of bows and arrows, slings, and triremes. However 
dishonest or prejudiced or stupid a wTiter may be, he cannot 
make any statement whatever about things that no one 
thought of in his time and country, he cannot give his story 
a general background absolutely different from that of his 
own direct or indirect experience, and he cannot write in a 
language that he never heard or read. 

To take a more concrete illustration of the same point. 



MORE REFINED METHODS. 3^3 

Suppose we have reason to believe that Paul really made the 
speech before Agrippa recorded in Acts xxvi., but have no 
reason to believe that he told the truth, we can still infer 
that Paul and Agrippa were contemporaries; that Paul was 
a prisoner wearing some kind of * bonds ' (v. 29); that he 
had been accused by certain Jews (v. 2) of some offence 
connected, or capable of being plausibly explained as con- 
nected, with their peculiar customs (v. 3) and religious beliefs 
(v. 7), and more particularly with his own real or assumed 
belief in the resurrection of the dead (v. 8) and with what 
he represented as the divine mission (vv. 15-22) of one Jesus 
of Nazareth (v. 9). If we have no reason to believe that 
this speech was ever made, but do know the time and place 
at which the story of the speech was written, then w^e can 
still infer that at that time and place people knew the 
names Paul, Agrippa, Festus, Jesus, Christ, Satan, Jerusalem, 
Damascus, etc. ; that they had either hoard of the Jews and 
their religious sects (v. 5) or had invented the idea; that it 
seemed to them credible that a Jew might be prosecuted and 
even put to death (vv. 10, 31) for a religious belief, and 
that a king would listen to a prisoner in bonds who talked 
of prophets, visions, repentance, forgiveness of sins, and the 
resurrection of the dead; that at least some of the people 
of the time and place where the story was written knew the 
meaning of the common terms used to denote such things, 
and that at least one of them was interested enough in these 
things to write down a long story that turns upon them — a 
story, too, that shows a strong sympathy for Paul, his hero, 
who is supposed to believe in them. 

In the example just given the method of causal inquiry 
by which we discovered some of the facts behind a story was 

very crude, and the results attained, thou2:h per- 
, . 1- . More re- 

haps important, were correspondingly meagre, fined me tli- 

The method was crude because it made use of 

no sources of information outside of the story itself^z*.^., it 

proceeded wholly from internal evidence — and because it 



374 TESTIMONY. 

took no account of the difference between different indi- 
viduals and the intimate surroundings in which they are 
placed. It took account of the fact that certain things, such 
as using a language that he had never learned, would be 
impossible for any individual whatever; but it did not take 
account of the fact that for this particular individual there 
must be other things w^hich are equally impossible. More- 
over, where each of several alternatives was possible — e.g,, 
Paul's sincerity or insincerity in the speech before Agrippa 
— it did not ask which was the most probable. 

Another thing to notice about the conclusions drawn in 
the example is that most of them have nothing whatever to 
do with the question or questions which we probably had 
in mxind when we read the story. If we are trying to find 
out something about the character or real beliefs of Paul, it 
does us little or no good to know that he was the hero of a 
story that may have been written hundreds of years after his 
death by a person w^ho knew nothing about him but his 
name, and that the audience for which this person wrote 
was supposed to be interested in discussions of sin, forgive- 
ness, and resurrection. Every story reveals something about 
the person who tells it, but it does not necessarily reveal 
anything — except that the author knew the name — about 
the persons or events of whom it is told. 

To learn anything from it about these persons or events 
we must find out who the author is and what relation he 
bears (or has borne) to them. If he knows nothing what- 
ever about them (except their names) we can learn nothing 
about them (except that their names were known in his time) 
from the story that he tells, however plausible it may be. 
If he has been in a position to know about them, so far as 
his external circumstances are concerned, but is too preju- 
diced m some particular direction to perceive or tell the 
exact truth, we may be able to find it from what he says if 
we can find out what his prejudices were and make proper 
allowance for them. If he really knows the truth but has 



MORE REFINED METHODS. 375 

such interests at stake that he will not tell it, we may get it 
from him in spite of all his efforts if we only know what 
these interests really are. 

In such cases of prejudice or falsehood we may get the 
truth from what the witness says, and if we have patience 
and ingenuity enough and if he talks enough, or if we know 
enough about him and about the surrounding circumstances, 
we undoubtedly shall. But in most cases this is too much 
to expect, and our knowledge or belief that the witness is 
prejudiced or untruthful only leaves us in doubt as to what 
the facts really are. On the other hand, if a witness who is 
in a position to know the facts is both unprejudiced and 
truthful, and if we know it, we are vastly better off. We 
expect him to make occasional blunders and so we cannot 
abandon the critical attitude altogether; but in the main 
our causal inquiry is greatly simplified. Instead of having 
continually to make uncertain allowances for some prevail- 
ing perversity that may (or may not) have affected this, that, 
and the other statement, we know that the vast majority of 
his statements are substantially true. Any given one of 
them may be more or less false, to be sure, and therefore if 
the matter about which it is made has intrinsic importance 
enough to justify the trouble, we must inquire further before 
we accept it. But if the witness has really been in a posi- 
tion to know and if he is really truthful and unprejudiced, 
there is no reason why all his blunders should lie in the 
same direction; and therefore when we care nothing about 
mere individual details as such, but only about the larger 
whole into which they are all combined, we may accept his 
statements as true enough on the whole for our purposes. 
We thus avoid the continual correction of details w^hich is 
necessary before we can get a true conception of the events 
as a whole from the story of one who is prejudiced or 
deliberately untruthful. The wall of a building may be 
plumb although every brick in it is a little out of plumb in 



376 TESTIMONY. 

one direction or another, but it will not be plumb if all the 
bricks incline in the same direction. 

To learn anything from a story about the facts of which it 
tells, our first task, as we have just seen, is to identify the 
Who is the witness. This does not mean merely to find his 
witness? name. It does not tell us anything about the 
truth of the Iliad to know that the author's name was 
Homer. Knowing who the witness, is means knowing all 
that we possibly can about his personality, his interests, 
and the circumstances under which he gained or expressed 
his ideas. If the Iliad is a work of pure fiction written 
centuries after the siege of Troy, it may reveal very much 
about some other time and place, but it can tell us abso- 
lutely nothing about what transpired at that siege. Many 
of the stories that we read and hear are precisely such pieces 
of fiction. Lawyers and historians know this, and therefore 
when a person is about to give testimony in a court the 
lawyers begin by asking his name, his residence, his busi- 
ness, his relations to the parties concerned, and so on; and 
careful historians do not try to extract information from a 
writing until they have asked similar questions about the 
author. 

In this matter of identity we must not take too much for 
granted. It is often in the interests of one individual to 
personate another or to forge his signature. The law recog- 
nizes this and guards against such deceptions as well as it 
can, not only by imposing heavy penalties upon those who 
commit them, but also by requiring that deeds be signed in 
the presence of a specified number of witnesses each of whom 
makes oath that the deed was signed in his presence and 
that he knows the persons who signed it. On the same 
principle, bankers require the identification of those who 
present checks for payment; society demands the proper 
introduction of all newcomers; and manufacturers are con- 
tinually warning their customers against ' spurious imita- 
tions \ Where there are no penalties for deception and 



WHO IS THE WITNESS? 377 

where no precautions against it were taken beforehand the 
need for caution is especially great. The historian in par- 
ticular should realize that the writings with which he has to 
deal often bear the names of some one who did not write 
them; for it is easy to ascribe manuscripts and works of art 
of unknown origin to some famous maker, just as it is easy 
to say that our rugs were made in the Orient or that our 
furniture and our ancestors * came over in the Mayflower'. 
It increases their value, and our friends are not usually very 
critical about such matters. But that does not make such 
happy fictions true. The older any manuscript or other 
possession appears to be, the greater is the danger that it 
has been assigned to the wrong person. 

One of the most famous examples of false authorship is the 
*' Donation of Constantine ". This remarkable document 
purporting to come from the early part of the fourth century 
was fabricated some time between 750 and 840, and imposed 
upon the world for six hundred years. In the document 
Constantine is made to tell how he was miraculously cured 
of leprosy by Silvester, the Bishop of Rome, and then to 
hand over his "palace, the city of Rome, and all the 
provinces, places, and cities of Italy and [sive'] the western 
regions to the most blessed Pontiff and universal Pope, 
Silvester . . . and his successors''. But the whole style of 
the document is that of the eighth or ninth century, not of 
the fourth; Constantine is made to describe himself as con- 
queror of the Huns, though they did not appear in Europe 
until at least fifty years later; Silvester is described as 
Summus Pontifex, though ' this title w^as still borne by the 
chief of the pagan college of priests ' ; the date wTitten in 
the document is impossible, for no such joint consulate as 
that mentioned ever existed ; and there are many other evi- 
dences in the document itself that it could not possibly have 
been written in the time of Constantine.* 

^ I have used part of the translation and criticism by Thomas Hodg- 
kin : -'Italy and her Invaders", Vol. VII, pp. 149 ff. 



378 TESTIMONY. 

In seeking the authorship of a writing we cannot even 
take for granted that the whole piece was the work of a 
jfjint single author. Sometimes a report which some 

autnorsMp. official signs is really the work of half-a-dozen 
different secretaries or departmental managers. Sometimes 
the principal author had a collaborator whose name does 
not appear. Sometimes, again, the original piece has been 
garbled by a copyist or an editor or a whole series of them, 
each one of whom made some stupid blunder or tried to 
improve the story. 

We cannot detect the work of different authors and editors 
in the same piece unless we assume that human beings are 
subject to the general uniformity of Nature, and that there- 
fore a person's vocabulary, style, knowledge, and interests 
do not change suddenly or without some adequate cause. 
To give an example. The play Henjy VIII. was assigned 
by the editors who first published it to Shakspere; but re- 
cent critics tend to divide it between Shakspere and Fletcher. 
The evidence for the division that they make is found partly 
in the form of the verse, Fletcher was very fond of lines 
ending with an extra, unaccented syllable; Shakspere was 
not. Fletcher generally made his phrases and sentences 
end at the end of a line; Shakspere not so often. Quite 
recently Professor Ashley Thorndike has discovered another 
test by which he confirms the division made on such grounds 
as these. He has noticed that, in the works about whose 
authorship there is no doubt, Fletcher almost always con- 
tracts the word ' them ' to ' 'em ', using the latter fourteen 
or fifteen times as often as he uses the former, while Shak- 
spere uses ' 'em ' rarely and ' them ' frequently; and he finds 
that the use of these words in each part of the play agrees 
with that of the author to whom the part is assigned.* 

A more complex example of the method by which a 
document is shown to be the work of several different 

* "The Influence of Beaumont and Fletcher on Shakspere", O. B. 
Wood, Worcester, Mass., 1901. 



JOINT AUTHORSHIP. 379 

authors and by which his own part is assigned to each is 
found in recent researches into the origin of the first six 
books of the Bible. According to the critics, or some of 
them, the composite character of these books is proved by 
such facts as these: (A) The "many unnecessary repeti- 
tions'' which they contain, e.g., the creation of beasts and 
birds in Genesis i. 21-25, ^^^ again in ii. 19, and of man 
in i. 27 and ii. 7; the story of the Manna and the quails in 
Ex. xvi and again in Nu. xi ; and the frequent repetition 
of similar laws in the legislative portions of the books. 
(B) "Frequent discrepancies and inconsistencies", e.g., 
the account of creation in Gen. ii. ^b and i. i to ii. ^a] 
different statements as to the duration of the flood; Abra- 
ham's incredulity about the birth of a son, Isaac, on account 
of his own advanced age, and yet his subsequent marriage 
after Sarai's death; the law that altars shall be of unhewn 
stone, unpolluted by the use of any tool upon them (Ex. 
XX, 24), and the directions for ornamenting an altar of acacia- 
wood (Ex. xxvii. 1-8). (C) " The want of continuity and 
order in the narratives, e.g., in the stories of Abraham, Noah, 
and Lot. The story as it stands in Ex. xix makes Moses, 
an old man of eighty, ascend and descend the mountain more 
than four times. (D) The "differences in style and con- 
ception ". According to the first chapter of Genesis man 
and woman are made together, apparently out of nothing, at 
the end of creation. According to the second, Adam is made 
first out of the dust of the earth and Eve is made last oat 
of his rib, when no helpmeet for him could be found among 
the brutes who were created in the meantime. " The first 
account is in form artificial and rhythmical, and the second 
graphic and picturesque." 

So much for the kind of evidence by which critics believe 
it can be proved that these books are not all the work of the 
same author. 

When it comes to the identification of the different authors 
whose work has been combined, it is necessary to study the 



380 TESTIMONY. 

documents much more closely. Throughout almost all of 
Leviticus and Numbers the writing is characterized by a 
' love of ceremonial law, fondness for statistical details, 
tendency to symmetry and similarity of phraseology, the 
insertion of the same or similar headings, and a style that 
in general is stiff and formal. When narratives occur they 
are little more than a collection of dry annals '. Moreover, 
the language of the original Hebrew shows certain pecu- 
liarities and uniformities. Since passages with these same 
peculiarities are found scattered throughout other parts of 
the Hexateuch they are all assigned to the same writer or 
group of writers, called P on account of his priestly ten- 
dencies. Since some of these passages written by P refer to 
what could not possibly have existed before the centraliza- 
tion of worship in the time of Solomon's temple, critics 
assume that they could not have been written before the 
building of that temple; and the relative maturity of many 
of the conceptions points to a much later date. From the 
minute directions as to the order and ceremony of worship 
critics infer further that P wrote at a time when such direc- 
tions were necessary — probably when worship in the temple 
had been interrupted by a period of exile — and so they infer 
that P's work is probably " the result of the religious move- 
ment which began with Ezekiel in Babylon and found its 
completion with Ezra ". 

The Book of Deuteronomy is as marked in its character- 
istics as Numbers and Leviticus, but very different. Its 
style is * smooth and flowing, redundant, pleasant to the ear, 
but sometimes tedious from the accumulation of synonyms \ 
Its aim is monotheistic and its character hortatory. It is 
remarkable for *' its tone of gentle pleading, its spirituality 
as regards both God and man. God has no outward and 
visible form; God is near man, and His law within man's 
heart ". It is " the Gospel of the Hexateuch ". From the 
presence of these and other characteristics so different from 
those of P, critics infer that Deuteronomy was written by 



JOINT AUTHORSHIP. 381 

another author, D; and they attribute to him or to others 
of his time and spirit the other passages scattered throughout 
the Hexateuch wliich are marked by the same peculiarities. 
Since D refers to the monarchy, the prophetic order and the 
priesthood of the Levites, it is inferred that this writer or 
group of writers could not have lived and written before 
these institutions were established. From the similarity 
between the spirit of D and that of the prophetic movement 
in the reign of Josiah and from other evidence it is inferred 
that Deuteronomy or some of it is the book of the law dis- 
covered in that reign, and written not many years earlier by 
some one who shared in the prophetic movement. 

When the writings of P and D are removed other passages 
still remain, and these seem to have been written at an 
earlier period. The institutions to which they refer are more 
primitive, and the language seems like that of one who is 
thoroughly familiar with them. These passages are supposed 
to constitute or to be taken from the old book of the 
Covenant, and are therefore denoted by the letter C; but 
when they are examined closely it is seen that they are not 
all alike, and the differences between them and the way in 
which they are combined seem to show that they are the 
blended product of at least two different writers in different 
periods. 

In one set of these remaining passages the name Jehovah 
(translated The Lord in our English Bible) is almost always 
used for God ; and God is given very human characteristics : 
He makes Adam out of the dust, walks with him in the 
cool of the evening, sends confusion of tongues to prevent 
the human race from becoming too strong, and has to go 
down to Sodom to find out what is taking place there. In 
this same set of passages the name Israel is used for Jacob, 
and Sinai for Horeb, Israel and other names are used col- 
lectively to denote the Sons of Israel and of other tribal 
ancestors, and there are certain peculiar phrases, such as 
*' to call upon the name of Jehovah '\ In thes^ passages, 



382 TESTIMONY. 

too, the narratives are always vivid and interesting and the 
conceptions are very naive, INIiracles, for example, are 
recorded without any insistence upon their miraculous char- 
acter, as though they were perfectly natural. These 
passages are therefore assigned to one writer, or group of 
writers, known from his name for God as J. In the other 
set of passages in C the name Elohim (translated God) is 
used instead of Jehovah, unless there is some special reason 
for using the latter; and God is conceived of as more separate 
from man than in the passages assigned to J, and not so 
human. Amorites are spoken of instead of Canaanites, 
Horeb instead of Sinai, Jacob instead of Israel (though not 
always), the word ' lord ' is used to mean husband, and 
there are other linguistic peculiarities. The style is more 
stiff and formal than J's and not so interesting, and the 
general conception of things is more sophisticated. When 
miracles are mentioned, for example, their miraculous char- 
acter is recognized and perhaps insisted upon. This second 
set of passages is therefore assigned like the first to a single 
author or group of authors, E. The greater naivete of the 
conceptions expressed by J indicate that he was an older 
writer than E, though the stories told by each of them 
probably originated at different dates, and some " were per- 
haps centuries old ".* 

For historical purposes it is often much more essential to 
distinguish the work of a given author from that of his 
editors than from that of his collaborators, for the latter at 
least were his contemporaries; and even though their state- 
ments may not be so trustworthy as those of the author 
himself, the ideas v/hich they express and the words in which 
they express them must have existed in the author's time 

■^ See Article Hexateuch, in the ^' Dictionary of the Bible ", published 
by T. & T. Clark in 1899. The account of Hexateuchal analysis whicli 
I have given in the text is, I hope, sufficient to give some idea of the 
method involved in such investigations. It is far too fragmentary and 
guperficial to be accepted as an accurate account of their results, 



JOINT AUTHORSHIP. 383 

and country. If we are fortunate enough to possess several 
different manuscripts which have descended through different 
editors from the same original, the agreements and differences 
between them wiil make it relatively easy to ' restore ' the 
original, or find what it really did (and did not) contain. 
If there is only one text, the task is harder, for we must 
depend altogether upon the same kind of data as those 
which must be used for the discovery of collaborators. But 
however difficult this work of restoration may be, it cannot 
be dispensed with if we wish to prove anything by the writ- 
ing in question; for a subsequent addition to a book proves 
nothing about the times in which the book itself was written, 
and the firmest possible faith in a given individual gives no 
ground for believing something that he never said. A 
writing whose authorship has been determined is said to be 
' authentic '. But this word does not imply anything about 
the truth of the statements that it contains. 

When the witness is identified, the author found, his text 
restored, what then ? If he has not been in a position to 
know anything whatever about the events of which he 
speaks, except perhaps a few names — that is to say, if his 
conceptions have not been caused in any way by these 
events — it may be worth while to account for his knowledge 
of the names, but otherwise we can learn nothing from him. 
If, on the other hand, he has been in a position to know 
about the events of which he speaks — if his story is in some 
way or other the result of an impression made upon him by 
these events — we must examine his account of them in the 
light of all that we can find out about the witness himself, 
his circumstances, the interests he had at stake, his preju- 
dices and his veracity, and thus try to discover the events 
themselves by finding the cause that would be most likely to 
produce the story that he tells. 

First the question of how the witness got his information. 
Witnesses do not as a rule discuss this question ; they simply 
speak with an air of authority which leads the unsuspecting 



384 TESTIMONY. 

hearer to assume that they know. If they do mention 
How does their sources of information, they generally make 
he know ? them appear better than they really are. A per- 
son may describe himself, for example, as an ' eye-witness ' 
of some great battle in which he took part. But a battle is 
much too large and complex an affair for any single individual 
to see the whole of it, much less one who is busy fighting in 
his own part of the field. Nine-tenths or more of what the 
' eye-witness ' probably tells about is therefore based upon 
conjecture or the confused tales of other combatants often 
heard at fourth or fifth hand. 

If a witness got his information through somebody else and 
if he is not himself a trained investigator, his statements must 

be taken with the greatest caution. This second- 
Hearsay. 

hand evidence, or " evidence which does not de- 
rive its value solely from the credit to be given to the witness 
himself, but rests also, in part, on the veracity and compe- 
tency of some other person ", is what is known to the law as 
' Hearsay '; and except in a few specified classes of cases our 
courts refuse even to listen to it. ^^The law requires . . . 
the testimony of those who can speak from their own per- 
sonal knowledge. It is not requisite that the witness should 
have personal knowledge of the main fact in controversy ; 
for this may not be provable by direct testimony, but only by 
inference from other facts shown to exist. But it is requisite 
that, whatever facts the witness may speak to, he should be 
confined to those lying in his own knowledge, whether they 
be things said or done, and should not testify from informa- 
tion given by others, however worthy of credit they may be." 
We do not reject hearsay altogether in common life, and 
there is no reason why we should. The courts can afford to 
do so because they give power to the litigants to compel the 
attendance of witnesses (if they are alive and within the 
court's jurisdiction) who can speak from their own personal 
knowledge. Moreover, in the courts the only matters which 
have to he proved by witnesses are those which one party or 



HOW DOES HE KNOW? 385 

Other is not prepared to admit. Thus the procedure of tlie 
courts does not imply that nothing can be proved by hearsay 
outside of them. It does show, however, that in the opinion 
of jurists hearsay is not in general a very satisfactory kind of 
evidence. The objections to it are the probability that the 
statement of the person quoted ^Svas imperfectly heard, or 
was misunderstood, or is not accurately remembered, or has 
been perverted "; the ease with which a lying wutness can 
shield himself when he says ' he was told '; the impossibility 
of cross-examining the person quoted, 'Hhat it may appear 
what were his powers of perception, his opportunities for ob- 
servation, hisattentiveness in observing, the strength of his 
recollection, and his disposition to speak the truth"; and 
the frequent impossibility of telling ^'through whon\, or how 
many persons, the narrative has been transmitted, from the 
original witness of the fact." ^ 

If we cannot tell an)lhing about the origin and history 
of a story, if we have no reason to believe tliat the person who 
tells it to us would sift it thoroughly before telling it, and if 
it does not bear som^e very strong internal evidence of truth, 

■^ Greenleaf, ''The Law of Evidence ", §§ 98, 99. The rule against 
the admission of hearsay does not of course exclude everything that a 
witness claims to have heard said. Evidence about the statements of 
another person is not hearsay when ^' the very fact in controversy is 
whether such things were written or spokeji^ and not whether they were 
true ". If a person is being tried for slander a witness would be allowed 
to testify that he heard him say the slanderous words ; but he would not 
be allowed to testify that some one else had told him that he had heard 
him say them. Again, evidence is not hearsay when the statements, 
whether written or spoken, which the witness repeats are " natural or 
inseparable concomitants of the principal fact in controversy ". In a 
murder trial, for example, a witness may testify that he heard the 
prisoner threaten to kill the deceased, not because there was necessarily 
any truth in the threat, but because it indicates a state of mind in which 
such a deed might be done. The threat is thus a part of the res gesice; 
it has, or may have, a direct or indirect causal connection with the act 
in question; and it is thus so much circumstantial evidence, not hear- 
say. 



3^6 TESTIMONY. 

we have no right to assume that it is true. This statement 
applies to the ordinary newspaper anecdotes about public 
men, to much of the gossip that we hear about our neighbors, 
and to almost all of the legends of ancient heroes and medi- 
aeval saints. 

Now comes the question whether a witness is truthful. If 
we are really weighing testimony, tliis question must be 
Is he truth- answered according to some rational principle. 
ftU? rj.^ depend upon our impulses for an answer is 

not to weigh it at all, but merely to return to the primitive 
condition in w^hich we were before we discovered the need 
for w^eighing it. Hence we must not assume that a witness 
is truthful merely because the story he tells is pleasant or flat- 
tering, or because it is interesting or pathetic ; because he is 
polite or intelligent, his voice and accent winning, or his 
manner confidential ; because he was hard to find, knows so 
much about the subject, or is perhaps the only person whom 
we can find that knows anything about it at all. We must 
not trust him either merely because he was doubted once be- 
fore and vindicated, or even because ' he told us himself he 
that was telling the truth ' . So, vice versa, we must not assume 
that a witness is untruthful or ignore w^hat he says merely 
because he is uninteresting or disagreeable. 

In the efi'ort to escape the influence of our impulses where 
impulses are liable to mislead, and to find some fixed test 
Arbitrary of veracity, there is danger of choosing something 
^^ ^* purely arbitrary ; of assuming, for example, that 

there must always be ' truth on both sides ' when witnesses 
disagree, and trying to split the difl'erence between them ; or 
I of assuming that the story supported by the larger number of 

witnesses must be the true one, regardless of the character of 
the individual witnesses and their sources of information. 
Because truthfulness is right and lying wrong, people have 
often invented arbitrary tests based upon the supposition that 
God would intervene in some particular manner to vindicate 
the right and punish the wrong. Thus a person sometimes 



IS HE TRUTHFUL? 387 

Says, ' May God strike me dead if what I say is not true ', and 
in a case of this sort if the calamity named does happen to 
occur it is often accepted by those who see it as a divine 
judgment. Such tests are easily systematized and adopted 
by a people as a whole. Consequently the Hebrews cast lots 
to discover a culprit, and our own ancestors in the middle ages 
appealed to the ordeal or to trial by combat. Such tests still 
survive, although the definite appeal to God may be lost ; 
and schoolboys assume that one of their number has ' de- 
fended his word ' or proved his truthfulness if he has won a 
fight with the boy who impeached it. In the same way when 
boys play the disputed part of some game over again, the 
winner announces that ^ that proves it '. 

If such simple methods as these for settling the rights of 
a case and the veracity of the witnesses had been found 
effective, the state and the church would certainly still con- 
tinue to use them. Nowadays, however, we recognize that 
God or Nature gives no arbitrary sign by which we can detect 
a lie and vindicate the truth. We are not left wholly without 
a test — far from it ; but the test which w^e have is hard to 
apply and, like the oracles of old, it often leaves us in doubt. 
There is no ultimate test of truthfulness but fact, and the test 
of fact is nothing less than consistency with the whole 
course of Nature. 

When the fact itself is unknown and we are trying to esti- 
mate a witness's veracity in order to find it, the most im- 
portant things to consider are his personality ; his special 
relations to the question about which he speaks ; the consis- 
tency and probability of the story he tells; and its relations 
to the stories of other witnesses. We must speak of each. 

First the witness himself. We must not judge everybody 
by ourselves. Whether a person has a strong disposition to 
speak the truth is largely a matter of his own in- 
dividual character. This is very different in dif- 
ferent people, and it is something about whicli we cannot 
always know. We often can know, however, about a per- 



3^8 TESTIMONY. 

son's race, the age in which he lived, his occupation, and the 
set to which he belonged ; and all these help to determine 
his veracity. An Oriental is generally less likely to speak 
the truth than a European, a slave than a master, a promoter 
than a military officer. If Othello had stopped to think, he 
might have known that an Italian of lago's time, even 
though an officer, would not hesitate to deceive a man of 
alien race if he had anything to gain by it. 

In considering the effects of character we must not assume 
that the most innocent persons are necessarily the most 
truthful. A child may tell the most harmful lies in all inno- 
cence simply because the thought has come (or been put) 
into its head, and he has not critical judgment enough to 
distinguish clearly between truth and falsehood or to recog- 
nize the wrongness of the latter. A child once more may lie 
from pure nervousness. Ask him in a threatening tone 
whether he has done some perfectly innocent thing which 
you have seen him doing, and very likely he will deny it. 

Next the circumstances. We must not divide people once 
for all into shee[) and goats, those who lie or prevaricate and 
Circum- those who do not. '' Falsus in uno falsus in 

stances. omnibus" does not mean that if a person lies 

once he will lie always, but only that he is likely to lie 
again on the same occasion and about the same matter. 
Conversely, though a person has never yet told a lie, he may 
tell one in some new situation where the strain is greater. 
There always must be first offences. Therefore, when we 
have estimated a witness's general character, truthfulness 
and characteristic motives as well as we can, we must try to 
find out what special circumstances are present to influence 
him. Much depends, for example, upon the solemnity of 
the occasion on which the statement is made. A person is 
not likely to lie when he is confessing to his priest or when 
he knows he is at the point of death. The law recognizes 
the influence of this solemnity, and therefore it demands 
that every witness who comes into court shall swear to tell 



INTERESTS. 389 

the truth ; -1^ but on the same principle it regards a dying 
declaration, even when the witness was not sworn, as equiva- 
lent to an oath. 

One of the most important circumstances which we have 
to consider is the effect which the witness expects his story 
to have upon his interests. If the story which he 

IntGrGsts 

deliberately tells is against his own interests or 
the interests of those whom he would like to help, and if he 
must realize this, it is much more likely to be true than if it 
were one which he probably believed to be favorable ; for 
people often lie to further their interests, but not to injure 
them. Here again the law recognizes our natural tendencies 
and attaches great importance to confessions of guilt or other 
statements against ones own interest, while on the other hand 
it has generally refused to listen to the testimony of any one 
who has a pecuniary interest in the result of a suit or to a 
prisoner who is on trial, regarding the latter' s plea of ^ not 
guilty ' as a plea only, or a demand that the charge be 
proved, and not as evidence. f 

While we may learn something from the procedure of the 
courts, we must be careful in this case, as in that of hearsay, 
not to infer too much from it. A court of law cannot admin- 
ister justice effectively (especially when the work is divided 

* The oath is intended to direct the attention of the witness to God — 
not to direct the attention of God to the witness. 

■(■ Dying declarations and statements against interest, including con- 
fessions of guilt, are two of the very few kinds of hearsay that the law 
admits as evidence. Of course the witness who tells of a person's ad- 
missions or confessions must have heard them himself and not merely 
heard some third person tell about them. 

The refusal to listen to an accused person is partly in his own interest. 
His testimony cannot help him very much in any case, for he would not 
be on trial if his word were not suspected ; and if he is really innocent, 
it may do him much harm, on account of the embarrassing circum- 
stances under which it is given. Hence in States where the prisoner is 
allowed to speak in his own defence the jury is warned that if he does 
not choose to do so, it must not be taken as any evidence of guilt. 



:^ 



39^ TESTIMONY. 

as it is in our system between a judge and a jury) unless it 
acts according to general rules ; and evidence which the rule 
excludes might sometimes be recognized as perfectly good if 
it could be considered on its individual merits. Again, as 
we said concerning hearsay, the questions of fact that juries 
have to settle are always disputed ; and rules which may be 
perfectly appropriate in settling disputes that the disputants 
cannot settle for themselves maybe quite absurd when applied 
to matters that were never disputed. Then, too, it must be 
remembered that a person is not usually brought to trial for 
an alleged crime unless there is at least some prima facie 
evidence against him, and that in every civil suit that turns 
on some question of fact, one of the two litigants must have 
a bad case and be trying wittingly or unwittingly to ' make 
the worse appear the better reason.' When both parties to 
a transaction are clear-headed and honest they are not likely 
to get into court about it. Even where misunderstandings 
arise people generally succeed in keeping out of court when 
they have confidence in each other's honesty and fair-mind- 
edness. Under these circumstances it is not unreasonable 
that the court should say : Often half of the parties interested 
cannot be trusted ; the jury — untrained as they are — cannot 
always tell from the way in which the parties give their evi- 
dence which half this is; we will therefore exclude the tes- 
timony of them all, and depend upon that of disinterested 
persons, whom we can nearly always summon, and whose 
average honesty and intelligence will probably approach 
nearer to that of the community as a whole. This is very 
far from meaning that a person should never trust his neigh- 
bor's truthfulness when the story told by the latter happens 
to be in his own interest. 

Though we need not always go so far as the courts of law 
and reject the evidence of interested parties, we must not 
neglect to make proper allowance for their interests. Most 
people who tell a story, whether it be written or spoken, 
have some object in telling it, even if it be nothing more 



INTERESTS. 39 1 

than their own temporary amusement or the entertainment 
of their hearers; and if the story is about some important 
matter, the chances are that the narrator has some personal or 
party interest which leads him, perhaps insensibly, to distort 
the facts a little for the benefit of his own ' side '. If he is 
writing a oiography of a deceased friend for circulation 
amongst his admirers, it is moderately certain that he will 
dwell upon his good deeds and leave as many as he can of 
the doubtful transactions out. His very purpose or prejudice, 
however, may make some of his statements all the more 
trustworthy. If he mentions a few ' regrettable incidents, 
due not so much to the fault of the deceased as to the very 
unfortunate position in which he was placed', or incidents 
for which he feels compelled to offer any other kind of 
apology, his reader can feel moderately certain that the in- 
cidents occurred. The reader can be sure at least that the 
author believed they did, and that he would probably not 
have believed it if the evidence had not been very strong. 

Special confidence in statements against the interests of 
those who make them is not deserved unless the speaker 
really knew or believed that they were against his interests. 
If a prisoner had been told that ' it would be better for him 
if he confessed ' or that if he did not confess he would be 
arrested (and if he had not been subsequently warned that 
anything he said might be used against him), a court of law 
would refuse to listen to the story of his confession. In the 
same way the disgusting story which some one tells of his 
own villainy must not be accepted with the confidence 
which naturally belongs to a confession unless it is disgust- 
ing to the narrator as well as to the hearer. It may be that 
he is really boasting. Again, a person may confess some 
fault that he never committed in order to gain sympathy by 
the very fact of confession or to show how good he is now, 
since he is willing to confess it, or how much he has changed. 
In a sentimental age confessions are not always hurtful. 
Once more, if a man takes sides against ' his own country ' 



39^ TESTIMONY, 

and attacks its leaders, what he says is quoted all over the 
world with the weight of a confession; and yet the man who 
does it may have divested himself of all special interest in 
his country, or this interest may be outweighed completely 
by the hostility which he feels towards the leaders whom he 
attacks, or by the pride which he takes in being thought 
' broad-minded \ These same considerations are applicable 
to the alleged confessions of ' converted ' nuns, priests, free- 
masons, and pagans. Finally, a confession should not 
carry much weight unless the person who makes it is in his 
right mind. It is not unusual for weak-minded persons to 
falsely confess hideous crimes of which they have read or 
which have taken hold in some other way of their imagina- 
tion. 

The only direct proof of a witness's truthfulness or un- 
truthfulness in any particular case is the agreement of his 

story with the facts themselves. We may reject 
Consistency . . , . ^ r ^ ^ i \ - 

and general his Story because we know beforehand that his 
probability. , . i i i i i i -, 

word IS not to be depended upon; but we could 

not know this unless we had been able to compare the stories 
which he told on other occasions with facts. 

A story contrary to fact must be false, and unless we are 
willing to abandon absolutely all tests of truth and truthful- 
ness we must be prepared to admit this, no matter how 
trustworthy the author of the story may have previously 
seemed to be. 

Of course a direct comparison with the facts in the case is 
impossible when these are unknown and it is through the 
story itself that we are trying to find them. But there are 
certain more general facts which we do know and with which 
every true story must agree. A story ' inconsistent with 
itself ' cannot be true because the alleged facts which it 
asserts cannot all coexist in a world ordered as we believe 
ours to be. On the same principle a story cannot be true 
which asserts the existence of any single state of affairs which 
is incompatible with the world's general arrangement. On 



CONFIRMATION AND CONTRADICTION. 395 

the same principle, finally, a story is probably false if it is 
like other stories which often grow out of the interests, 
prejudices, or vanity of such narrators as the witness, under 
circumstances like the present, but which are seldom true. 
This is the justification for incredulity towards tales of 
extraordinary luck in fishing, of wonderful hands in cards, 
and of remarkable coincidences that the narrator attributes 
to occult causes. By saying that stories of this third sort 
are probably false we do not mean that any given one of 
them is false, for we expect the most improbable of possible 
events to happen some time or other. We only mean that 
a person who never believes such stories in the absence of 
exceptionally strong evidence will be right oftener in the 
long run than one who generally believes them. 

If there is any reason why a witness should not wish to 
tell the truth, the falsity of a part of his story may be suffi- 
cient to show that he is probably untruthful and therefore to 
discredit all the rest. But the falsity of one part of a story 
is not sufficient in itself to prove the falsity of the rest. A 
person may have some prejudice which prevents him from 
seeing some one part of the facts and yet be perfectly able 
and willing to tell the truth about other parts; or he may be 
w^illing to tell a * little ' lie, but not to tell a ' big ' one. 
Even when a witness is perfectly unprejudiced and perfectly 
honest a certain amount of error and consequent inconsist- 
ency in his story is almost inevitable, — so much so indeed 
that a story w^hich is absolutely glib and consistent often 
seems too studied to be perfectly true. 

It is much easier to judge of the veracity of a witness if 
we are able to compare his story with that of others. When 
several independent witnesses agree in their confirma- 
stories they ' confirm ' or strengthen each other; cont^dic- 
and the more of such witnesses there are the ^ion. 
more likely is the story to be true; simply because each new 
witness makes it so much harder to account for the agree- 
ment on any other hypothesis. We must be quite sure, 



394 TESTIMONY. 

however, that the witnesses really are independent. If they 
tell precisely the same story in much the same words — if 
they use the same strange phrases or make the same im- 
probable blunders, like schoolboys who copy each other's 
examination-papers — it is practically certain that they are 
not independent. In that case they no longer confirm each 
other: there is really only one story, which they have all 
learned to repeat. In matters of this kind, however, some 
writers of history are very careless; for it is not at all un- 
common to find one citing a whole series of ancient authors 
or ' authorities ' in support of some statement, when there 
is not the slightest doubt that they all got the story from 
the same source. 

. Discrepancies, when they are found between the stories of 
several witnesses who speak about the same affair, may or 
may not indicate that at least one of the witnesses is prob- 
ably dishonest. If they do and if the witnesses are evidently 
working together, this may discredit them all; for a perfectly 
honest man with a true story will not ask or accept the 
assistance of a dishonest man with a false story. But if there 
is no evidence of collusion between the witnesses themselves, 
the dishonesty of one ought not to discredit the others, 
though it might perhaps discredit the person who summoned 
them all. It would be a gross fallacy to use Peter's story 
(on the assumption that it is true) to discredit Paul's and 
then use Paul's to discredit Peter's. 

As we can judge something about the truth or falsity of a 
story from its confirmation or contradiction by other stories, 
so likewise can we often infer something from the lack of 
such confirmation or contradiction. The importance of 
some events is so great and their consequences are so 
apparent that, if they happen at all, they are certain to be 
known by a vast number of people and referred to in one 
way or other by many of them. If an alleged event of this 
character is mentioned by only one out of a large number 
of contemporary writers, it is a fair conclusion that he is 



CONFIRMATION AND CONTRADICTION. 395 

romancing. So with contradiction. If a story that almost 
certainly would be contradicted if false is not contradicted, 
that affords some evidence of its truth. We must be careful, 
however, not to rely upon these tests where they are not 
applicable. People do not usually contradict newspaper 
anecdotes, or libels that they think beneath their notice. 
They certainly cannot contradict charges of which they are 
not told. Sometimes, moreover, a story is contradicted but 
we do not hear of the contradiction. Much the same is 
true, mutatis mutandis, of confirmations. 

Sometimes the nature of an alleged event makes confirma- 
tion or contradiction of the story told about it absolutely 
impossible. If Elijah was alone at Horeb, as the story 
seems to imply, a hundred different documents could give 
no confirmation to the statements in I. Kings xix about 
what happened to him there. The most they could possibly 
prove would be that the writer in Kings had correctly stated 
Elijah's own account of it. In the same way, a hundred 
other ' accounts ' of the event could not prove that Elijah's 
story was false, though they might prove that he did not tell 
the story as it is given in Kings. 

Before one story can confirm or discredit another, it must 
be clear that the events to which the two refer are the same. 
This cannot always be taken for granted. Because A and 
B both say they saw a woman fall as she was getting off a 
street-car in the city yesterday we have no right to assume 
that they must have seen the same accident, for events of 
this sort are common enough and often very similar. In 
the same way, we have no right to assume without further 
investigation that there is any connection between the story 
of a flood told by some tribe of North American Indians and 
that told in Genesis; for there are certain types of story that 
we expect to find everywhere — stories of a creation, of a 
great flood, of the origin of speech and of fire, of a very 
strong man, a very wise man, a very faithful friend or lover, 
of talking animals, ghosts, giants, and the good old days, 



39^ TESTIMONY. 

Such stories are developed by a common mental process out 
of the common elements of human experience. The only 
way to prove an historical connection between two similar 
stories of this sort from the stories themselves is to show that 
there is more similarity between their details than the general 
similarity of human thought and experience will account 
for. It is not remarkable that the Hebrews and the Greeks 
should both have stories of a wise man and of a faithful 
friend; but it is curious that the names Solomon and Solon, 
David and Damon, should be so similar, and a few more 
coincidences of this sort would suggest very strongly some 
historical connection between two sets of stories or the 
events on which they are based. 

So much for the tests by which we judge of the veracity 
of a witness and the probable truth or falseness of his story. 
If these tests give us reason to believe that he was in a posi- 
tion to know about the matters of which he speaks and that 
in the main he is unprejudiced and truthful, the task which 
remains for us is comparatively easy. But if we have found 
that he is prejudiced or untruthful, it is not necessarily hope- 
less. In this case (as in the oth^r) we are far better off when 
we have the accounts of several different witnesses than when 
we have only that of one, no matter how prejudiced or 
untruthful we may believe each one of these different wit- 
nesses to be, or how conflicting their stories are. For every 
lie must be made to fit somehow or other into a background 
of truth. The person who tells it lived in a real world and 
he is bound to express his ordinary conceptions of that world 
up to the point at which he thinks it necessary to falsify 
things in order to make his principal lie seem consistent with 
itself and with admitted facts. Different persons lying 
about the same event (however much they may agree about 
the main point at issue) are bound to connect the false state 
of affairs which they allege with the true which they take for 
granted, in different ways; and if each of them is cross- 
examined carefully enough, they will probably reveal enough 



THE JUDGE MUST JUDGE IMPARTIALLY. 397 

between them to make it perfectly plain what the truth must 
have been. In this case, as in every other, the more eff'Xts 
of a given cause we know the more likely we are to find out 
what the cause itself really was. When a person merely 
wishes to absorb the truth from others a contradiction 
between them is necessarily very embarrassing; but when he 
is trying to find the cause that lay back of their statements 
it may be very helpful. 

To what has been said about the principles by which evi- 
dence should be weighed I should like to add a few words 
about the attitude of the judge who has to apply them. 

If anybody wishes to have a question settled on its merits, 

he must make sure, to begin with, that the judge or jury to 

which he submits it is not so incompetent, 

The judg^e 
dependent, interested, or prejudiced that the inustjud§:e 

investigation will be a mere mockery. The State 
tries to provide for this by appointing judges who are learned 
in the law, and often by appointing them in such a way and 
for such a period that they will be independent of those 
whose cases they have to judge and of popular whims in 
general ; by refusing to accept as a juryman any one who has 
any personal interest in the outcome of a case or who has 
already formed an opinion upon its merits; by providing that 
law}/ers shall not ask ^ leading questions ', or those which 
indicate to the witnesses by their form what answer is 
desired; and by visiting severe penalties upon any one who 
attempts to ' tamper' in any way with judge, jury, or wit- 
nesses. In the settlement of our own problems we must 
not forget to take similar precautions. If the question is 
one v/hich demands special skill (whether it be in medicine or 
in morals), we should choose our judge w^ith reference to his 
skill, not with reference to the decision that we think he 
will give. It we desire an estimate of our own conduct, we 
should not go for it to our admirers or dependents, to those 
who have not the courage to form an opinion of their own 
and tell us what it is, or to those who cannot condemn or 



39^ TESTIMONY. 

approve of what we have done without also passing judg- 
ment upon themselves. When we have chosen our judge 
we must put our questions fairly, in such a way as to bring 
out the opinion held by him, and not in such a way as to 
tempt him merely to echo the opinion held or desired by us. 
We must not therefore say to him, ' Isn't this true ? ' or 
* Don't you think so ? ' and we must not beg him not to be 
' too unfavorable ' or ' too hard on us '. When all that we 
seek is an opinion it is absurd to bribe the judge and then 
congratulate ourselves upon his decision. 

When we ourselves are called upon to act as judges we 
must strive hard to resist not only the importunities of those 
According to who appeal to us, but the influence of our own 
evidence. desires and prejudices as well. Like good old 
Locke we must be able to say in all sincerity, *' It is truth 
alone I seek"; and we must be prepared to judge of the 
tcuth by the evidence, not, like sentimentalists, to ignore 
the evidence or discredit or distort it because it is not what 
we should like. If we have interests, prejudices, or 
cherished beliefs which are affected by the issue, we must 
deliberately force them aside until after the decision has been 
rendered. We must not heed the ' appeal to consequences ', 
which points oat that if we believe one thing we shall be 
forced to believe something else also which is unpleasant, 
though not necessarily untrue. If the affair touches us and 
those we love and honor so deeply that we cannot cast aside 
these interests and prejudices until the decision is given, 
then we must recognize that so far as this question is con- 
cerned we are not proper judges, and leave the decision to 
some one else. 

Again, when we ourselves have been called upon to decide 
a case (whether it be to determine some fact itself or to dis- 
cover what authority is best fitted to determine 

Must judgre jA we must not forget that for the moment at 
for himself. / ... 

least we have assumed a position of independ- 
ence, and we have no right to quietly abandon this position' 



MUST JUDGE FOR HIMSELF. 399 

until our task is finished or definitely given up. Tlie 
decision which we reach must be based upon facts, and the 
burden of drawing the inference from the facts rests upon 
us and not upon anybody else. To find the facts from 
which an inference can be drawn it is our right and our duty 
to get all the testimony we can; but when a witness has 
given us all the facts that he knows we have no right to ask 
what inference he draws from them, and then merely absorb 
his opinions, any more than a lawyer has the right to ask a 
witness whether he believes the prisoner is guilty instead of 
merely asking him what he saw the prisoner do, and leaving 
the question of guilt to the jury. If it is we w^ho are called 
upon to decide, even an expert cannot relieve us of our 
responsibility. A lawyer has a right to ask an expert on 
gunshot wounds how far the muzzle of a gun must have been 
from the body of the deceased when he w^as shot; but he 
has no right to ask whether the witness believes that the 
prisoner killed him. This is the question which the jury 
must settle — and settle for itself. So, likewise, if you happen 
to be a director in a company, it is your business to ex- 
amine the accounts yourself and see that everything is right. 
If there is anything which you do not understand, you 
must insist upon having it explained, not merely to the 
limit of the manager's patience, but to your ow^n full satis- 
faction. It is your business to judge for yourself, and you 
are not doing your duty if you merely accept his assurances 
that everything is satisfactory. The tendency to ask, ' What 
do you think ? ' and then chime in with the answer, no 
matter how little it is worth, is well illustrated by the story 
of the Frenchman who thought he would play a trick on his 
fellow townsmen, and went up the street telling everybody 
he met that there was a whale in the harbor; but when the 
crowd going down to see the whale became very large he 
concluded that the report must have some truth in it, and 
went himself. 

We can absorb real or pretended opinions, but we cannot 



400 TESTIMONY. 

weigh evidence, without a definite problem. Therefore 
whenever we assume the independent position of 
problem^d ^ j^dge we must begin by finding out precisely 
det^ite. what it is that we have to decide. This is often 

difficult; for we cannot make our questions 
definite until we know many things about the matter with 
which they have to do. We must therefore keep reframing 
the vague questions with which we started and making them 
more and more definite as our knowledge of the subject 
increases. The more light we have already obtained upon 
a subject the more we can break our questions up, and the 
more we break them up the more light we can obtain. 
Hence the saying that it is as hard to state a question 
properly as it is to answer it. In law there is a whole system 
of ' pleadings ' which must be conformed to in every civil 
suit and which has been devised for the express purpose of 
compelling the parties to come at last to some one definite 

* issue ' upon which the whole case turns, so that it all may 
be settled upon the strength of argument "^ (if it be a ques- 
tion of law) or of testimony (if it be a question of fact) upon 
this one single issue, and not in a loose way upon the case 
as a whole, f In history or in science we cannot always 

* This distinction between ' argument ' upon a ' question of law ' and 

* testimony ' upon a ' question of fact ' is purely technical. The true 
meaning of the law, as intended by the lawmakers or as decided in 
previous cases, is as much a question of fact as anything else, and the 

* argument ' addressed to the judge is a presentation and explanation of 
the evidence as to what this meaning is, precisely as the examination of 
witnesses and the address to the jury is a presentation and explanation 
of the evidence concerning other facts. 

f Civil suits and criminal proceedings must always be based upon 
something definite. No court will entertain a suit for general injuries 
or a charge of general misconduct. When the plaintiff — to take a 
civil suit — has made his definite ' declaration ' he must serve notice of 
it upon the defendant. If the latter makes no reply within a specified 
period, the case goes against him by default. If he makes one, it must 
be as definite as the charge. ( i a) He may ' demur for matter of form ', 
or say that the charge has not been made in legal form, perhaps, for ex- 



MUST HAVE A PROBLEM AND MAKE IT DEFINITE. 40 1 

reduce everything to one single question, for our interests 
are manifold and one aspect of a case may be quite as inter- 
esting as another. Yet we can separate our questions and 
discuss them one at a time. Often, too, we can find some 
one ' crucial test ', like the evidence which settles the vital 
issue in a lawsuit, by which each one of them can be 
settled. If we have too many questions in mind at once, 
whether they be relatively independent or whether several of 
them be subsidiary to some other, we are almost certain to 
become confused or to neglect some aspects of the case 
without knowing it, and thus to do bad work. The only 
safe method is to follow the example of the courts and hear 
only one case at a time, reduce this case to as simple an 
issue as possible, and dismiss as ' irrelevant ' every alleged 
fact that does not bear directly upon this issue, however 
interesting the fact may be in itself and however important 
for the settlement of some other issue. 

The lack of a definite problem reduced by successive 
analyses to one or more definite issues, and the lack of the 
consequent sense of relevance and irrelevance, is particularly 

ample, that it is too indefinite, (i b) He may ^ demur for matter of sul)- 
stance ', or say that there is no reason known to the law why he should 
not do the very thing charged against him. (2) He may * plead by 
way of traverse ', or say that he did not do the very thing charged. 
(3) Finally, he may ' plead by way of confession and avoidance ', or say 
that he did do it; but that there were certain other facts, which he speci- 
fies and stands ready to prove, which change the legal aspect of the case. 
By compelling the defendant to make some one of these answers to the 
charge and then compelling both sides to stand by the question which the 
pleadings have developed, on pain of losing the case, the court succeeds 
in reaching an issue of law or of fact about which the two sides differ, 
and which is definite and simple enough to be settled reasonably. If the 
final issue be one of law — raised by a demurrer — it is settled by the 
judge after he has listened to argument. If it be one of fact, it is settled 
by the jury after they have listened to the evidence. In either case the 
argument or the evidence (as it may be) is addressed to the particular 
point at issue, not to the case as a whole, and upon it the whole case 
depends. 



402 TESTIMONY. 

apparent in most discussions of politics and history. When 
it comes to these subjects the emotions connected with our 
party interests and party traditions make analysis especially 
difficult. There is nothing in a chemist's emotions to keep 
him from regarding a pail of water as really consisting of so 
many separate atoms of oxygen and hydrogen ; but if a person 
has been brought up to revere the Roman Catholic Church 
or to hate the Democratic party, there is much in his 
emotions to prevent him from regarding the one or the other 
as nothing but a number of separate individuals who differ 
greatly from each other in many ways and are determined in 
their acts by all sorts of different motives and external influ- 
ences. What is true of groups of persons is true also of 
groups of events. If we are accustomed to feel strongly 
about some great historical movement, like the Reformation 
or the Civil War, our emotions make it difficult for us to 
analyze it into several long series of separate acts, and to 
realize that while each individual act has its own particular 
moral relations the sum-total can hardly be said to have any 
whatever. 

Having made our question definite we must not attempt 
to answer it from the impression that the evidence made 
Issue before before we did so; for we only attend to the parts 
evidence. Qf ^ story that interest us, and details which may 
be of the highest importance for the settlement of some par- 
ticular point may be very uninteresting in themselves, and 
therefore pass unnoticed when they are told before the point 
is raised. The only thing to do is to go over every bit of 
the evidence again with each new question and pick out the 
parts that have a bearing on it. Moreover, we should do 
this again every time an issue is split up into others more 
definite, or abandoned for others more appropriate. A story, 
for example, which was rejected as false in the preliminary 
stages of an inquiry may contain some phrase or some 
allusion that will explain the whole matter when the problem 
is reduced to its last analysis. This process of going over 



MUST NOT BE MANAGED BY THE WTrNESSES. 4^3 

all the evidence afresh with each new question is not so 
tedious as one might suppose, for the new question always 
makes us see the evidence in a new light. 

The strength of our natural tendency to decide a case by 
our first impressions and to neglect the later evidence is well 
recognized by those persons who take care to have their own 
version of some quarrel told first. Here again the law 
recognizes our weakness, and not only provides that the 
judge and jury shall alwa^ys hear both sides of a case, but also 
determines the order in which they shall be heard, and pro- 
vides that after the evidence has all been given each side 
shall have an opportunity to review it and point out its 
bearings. 

When we are determining the precise nature of our 
problem'and sifting the evidence by which it is to be settled, 
the witnesses with whom we have to deal will Must not be 
often try to mislead us. They will appeal to ^e^wit-^"^ 
our emotions. They will try to make us sub- ^^^ses. 
stitute some other issue for the real one. They will intro- 
duce all kinds of irrelevant matter to distract our attention, 
and when they do they will make it as interesting as they 
possibly can. At the same time they will pass as lightly and 
indifferently as possible over the points which are of real 
value for the decision of the case. If they are compelled to 
dwell upon them, they may try hard to make what they have 
to say so tedious that we w^ill not listen to it, or so obscure 
that we shall stop trying to understand it. But in spite of 
all these artifices we must never let a witness determine what 
issue or what part of the evidence we shall attend to. To 
be sure we cannot pat him on the rack to make him tell 
the truth ; but we must always remember that it is we and 
not he who is judging, and therefore we mtist not say ' Yes ' 
when we do not understand ; we must not be afraid to cross- 
examine him on the points that we think essential (instead 
of those on which he invites us to examine him) ; and we 
must not stop the examination when the witness seems to 



404 TESTIMONY. 

think it has gone far enough, for fear that if we do not he 
will think us hostile or distrustful or stupid. 

Finally, if we really mean to settle our questions rationally, 
we must never settle them while we are confused or excited 

or while there is reason to believe that we have 
decide in a not yet found or sifted all the evidence worth 

considering. The impulse to have done with 
deliberation and get things settled one way or the other is 
very strong, and like every other impulse it has its value; 
but when we set out to decide a question on rational grounds 
it is out of place and we must resist it. Strangely enough, 
when we are trying to discover new truths the very presence 
of this impulse is the best possible sign that we should act 
against it, for it only arises when all the evidence will not fit 
together easily according to our preconceived notions, and 
that is the only circumstance under which there can be any- 
thing essentially new to discover. We must resist also the 
tendency to be hurried by the impatience of others. We 
cannot yield to it without sacrificing the independence which 
it was necessary to assume when we set out to judge for 
ourselves mstead of blindly following the leader or the crowd. 
Indeed the attempts which others make to hurry us are 
sometimes only a device to keep us from finding the truth. 
If in any particular case there is not enough evidence to 
settle a question rationally, we should leave it unsettled — not 
settle it irrationally. A good way to guard ourselves against 
the tendency to jump to conclusions when the evidence is 
only half weighed is always to ask whether the evidence on 
which we act would satisfy some cooler critic to whom we 
might submit it. The best judges are those whose decisions 
are reversed least often by the higher courts. 



CHAPTER XXXVI. 

THE THREE ULTIMATE TESTS OF TRUTH. 

Much has been said in the foregoing chapters about ways 
of testing truth. Something must be said now about the 
ultimate tests to which all others can be reduced. Of these 
there are three : Consistency, Conceivability, and Uniformity 
including Simplicity. We apply the test of consistency be- 
cause we are rational beings who recognize that two incom- 
patible states of aifairs cannot both exist ; we apply the test 
of conceivability because we have the gift of imagination as 
well as reason, and we believe that if certain relations are not 
imaginable, they cannot exist ; and we apply the test of uni- 
formity and simplicity because as active beings it is easier for 
us to do something old and simple than something new and 
complex. These three tests may not be equally decisive, but 
each has its own sphere, and in that sphere it is the best that 
we can get. 

The test of Consistency was considered at length in the 
discussion of deduction. We saw that statements may be 
regarded as inconsistent not merely when they 
directly contradict each other, but also whenever 
one of them asserts the existence of a state of affairs that is 
incompatible for any reason whatever with the state of affairs 
asserted by the other. We saw, too, that in order to tell 
whether one supposed state of affairs really is incompatible 
with another we must know something about how the world 
is actually constituted. This appeal to the actual constitution 

405 



4o6 THE THREE ULTIMATE TESTS OF TRUTH. 

of things vastly increases the number of cases to which the 
test of consistency can be applied ; but it cannot help weak- 
ening it, for there is always a question of whether things 
really are constituted as we suppose, and before this question 
can be answered we are often thrown back upon one or both 
of the other tests, and that, too, perhaps by some process 
that is vague, indirect, or complicated. 

The test of Conceivability, or rather of Inconceivability, 
for it is the negative relation that is decisive, is illustrated 
Conceiv- t)est in geometry. We believe that two straight 
ability. lines cannot enclose a space, because we cannot 

possibly imagine or picture two lines which look straight — 
i.e., look as though they ran evenly in one direction through- 
out their whole course — and at the same time look as though 
they enclosed a space. We believe that the circumference 
of a circle is curved in one place precisely as in another be- 
cause we cannot possibly picture a figure that looks as though 
it conformed with the ordinary definition of a circle — i.e., 
looks as though every part of the circumference were exactly 
the same distance from some one point within it — and at the 
same time looks as though the curvature of the circumference 
were not the same throughout ; and because the more unequal 
the curvature of a circumference appears to be the more un- 
equal also appear to be the radii. 

What is true of the definitions, axioms, and postulates of 
geometry is true also of the demonstrations. They too appeal 
to the fact that we cannot picture it otherwise. Suppose it is 
a question of proving that the three angles of a plane triangle 
are together equal to two right angles. The student goes 
through the demonstration with reference to the figure given 
in the book, and then if he is not convinced he tries to draw 
some kind of triangle to which the demonstration will not 
apply, and he feels sure of the demonstration only when he 
has convinced himself that no matter how hard he tries he 
can never imagine a plane triangle so drawn. Thus the first 
principles and the demonstrations of geometry both depend 



CONCEIVABlLll'V. 4^7 

upon certain limitations of our imagination. We believe 
them to be true because we cannot picture the contrary. 

There are two objections that may be raised against geom- 
etry as a demonstrative science. The first is that there may 
not be such a thing in the whole world as an absolutely 
straight line, an absolutely round circle, an absolutely per- 
fect triangle, and so on. How can we say^ the objector asks, 
that things must be so when in reality they may never be so ? 
The second objection is this: Even if our geometrical con- 
ceptions do agree with things as they happen to exist in this 
world, how can we say that anything viust agree with these 
conceptions when for all we know there may be some other 
world in which they do not agree at all — some world in which 
straight lines can enclose spaces and in which plane triangles 
do not have their three angles together equal to two right 
angles ? 

The answer to the first of these objections is that geometry 
is not primarily concerned with the question of whether 
things have certain forms or not, but only with the mutual 
relations of those forms themselves as we have to conceive 
of them. It does not say that such things as perfectly 
straight lines exist in the real world, but only that if they 
do, no one or two of them can enclose a space ; and to 
find out what a straight line is we go to our own imagina- 
tions, and not to the world of reality. It is true that 
geometry uses real diagrams, but the force of a demon- 
stration does not lie merely in the fact that we cannot put a 
certain combination of relations on a blackboard or a piece of 
paper without also putting in a second or leaving out a third; 
but rather in the further fact that we cannot imagine what 
the impossible combination would be like if we could put it 
there. It is not the physical impossibility, but the incon- 
ceivability, that appeals to us. If it were a mere question of 
physical fact, the force of every demonstration would depend 
upon the accuracy with which the figures are ruled and meas- 
ured; but it does not. Whether perfectly straight lines and 



4o8 THE THREE ULTLMATE TESTS OF TRUTH. 

perfectly round circles are ever found in the world is a ques- 
to be settled outside of geometry and wholly irrelevant to it. 

As to the other objection — that in some other world the 
fundamental relations of figures in space might all be turned 
topsy-turvy — the answer is that if it were so and if we were 
moved there, unless we also were changed we could never 
see it. We should undoubtedly find that things did not 
come out as we expected, and it might be that we could 
stumble across some algebraic formulae (like those applicable 
to the "fourth dimension") by which we could learn to 
adjust ourselves to their vagaries; but unless we ourselves 
were transformed or enlarged along with our world we 
should be no more able to see and imagine the new relations 
than a musician can hear and feel perfect harmony and 
melody in the chaotic strumming of a child. If we picture 
things at all, we have to picture them as we can. When we 
talk about lines and size and shape and direction our words 
have no meaning unless they refer to something which is at 
least partly picturable; and if we cannot even begin to pic- 
ture a kind of shape or direction that meets a given descrip- 
tion, we have a right to conclude that it is not picturable 
and therefore is not really a shape or direction at all. And 
this is just as true whether the shape and direction spoken 
of are supposed to be only imaginary or to be real. So that 
the test of conceivability which is applicable in the first in- 
stance to mere images as images can be applied also to the 
relations of things which are assumed to be imaginable. 

The danger attending the test of conceivability is that 
we may apply it where we should not. Geometry deals only 
with the arrangement of points and lines in space, and if 
some relation has nothing to do with space, we must not 
deny its existence because we cannot make a drawing of it. 
Nobody denies the existence of a song because the tones 
cannot be arranged in triangles and circles, or of a feeling 
of remorse because we cannot picture it as lying to the right 
or to the left of the knowledge that goes along with it. In 



THE THIRD TEST. 409 

the same way no one has any right to deny the existence of 
a soul merely because we cannot represent it as round or 
square, yellow or green, loud or soft, or literally sweet or 
sour. 

Our third ultimate test of truth depends upon our animal 
organization as creatures who form habits and ^he third 
tend in other ways also to do whatever must be ^^^t- 
done for our preservation and welfare, in the shortest and 
easiest way possible. 

We have seen how the tendency to make uniform reactions 
leads to the judgment that what we react upon is uniform, 
and how this uniformity that we find because we look for it 
is thought of as involving a vast number of permanent 
Things, each of which belongs to some definite Kind, and 
acts in the same Way as every other member of the Kind 
under the same Conditions. We have seen, too, how some 
apparent anomaly is ' explained ' when it is shown that in 
spite of appearances it is still a case of these same uni- 
formities; and how an interpretation of any particular ex- 
perience which cannot show how that experience grows out 
of these uniformities is branded as false and unhesitatingly 
abandoned for one which can. 

But the test of truth growing out of our organization as 
active creatures does not end here; for it may be 
that each of two or more explanations of an jJfthe"Sass. 
experience is consistent with these uniformities, 
and still we are able to choose between them, even though 
it be without quite so much certainty. 

It will be remembered that we came to seek for uniformity 
in the ultimate elements of which things and situations are 
composed because we were often disappointed in our efforts 
to find it in the complex things and situations as a whole. 
But it was in the complex mass that we looked for it at first. 
The first things that we notice and learn to separate from 
the confused mass around us are not definite details which 
we afterwards build up into more complex wdioles, but more 



41 o THE three: ultimate tests of truth. 

or less vague wholes which we afterw^ards analyze into the 
more definite details: we can recognize a person as a whole 
before we can describe a single feature. And so the first 
uniformities we expect are not uniformities in the definite 
details that we have not noticed, but in the vague wholes 
that we have. When two wholes present about the same 
general appearance they call from us the same rather vague 
and clumsy act, and we never think of fine distinctions 
between either the wholes to which we react or the reactions 
themselves until we find that a reaction which gives us what 
we want in one case will not do so in another. Then per- 
force, we are driven to notice some detail in which the two 
cases differed; and by a repetition of this process we reach 
at last the ultimate things and relations to which we feel 
that the law of uniformity applies without exception. 

But in spite of the disappointments which teach us that it 
is only in the ultimate details that we can be absolutely 
certain of our uniformities, we still continue to look for them 
with considerable confidence in the mass also. ' Appear- 
ances ', or general impressions, would not be ' deceitful ' if 
they never deceived; and they could not deceive if we had 
no tendency to trust them. We should not hear people say, 
' It is strange how much difference a little thing often 
makes,' if they were not in the habit of ignoring the little 
things and looking at the larger wholes. 

Thus we never lose the tendency to look for uniformity in 
the general appearance of things as well as in their ultimate 
relations, and thus it happens that when there are two possi- 
ble explanations for some state of affairs which are equally 
satisfactory in the various details, we naturally choose the 
one which gives the greater impression of uniformity in the 
mass. The ' catastrophic ' theory of the earth's history, 
which supposed the structure of its crust to have been pro- 
duced by a series of changes more violent than those with 
which we are familiar, might have given a perfectly satis- 
factory account of all the details under consideration, and yet 



UNIFOKMITV IN THE MASS. 41^- 

it would still have been abandoned as soon as Lyell showed 
that these details could all be accounted for just as well — 
I do not say better, for that is not my point — by processes 
of the sort that are going on around us all the time. 

This tendency to prefer accounts of things which make 
what is distant in time and space as similar as possible to 
what we perceive about us is due in part to the law of 
association. The feeling of belief is subject to this law like 
any other thought or feeling; and the more a new concep- 
tion is like one we are accustomed to believe in, the more it 
tends to arouse the same feeling of belief by its very likeness. 
In the same way, if a new conception bears a strong total 
likeness to one which we are accustomed to reject, we tend 
through the law of association to reject it. We act towards 
ideas precisely as we act towards people, liking those that 
look like our old friends, and disliking those that bear a 
strong resemblance to our old enemies. 

Another reason why it is easier to believe in things like 
those to which we are accustomed than in those that are 
not is that it is easier to conceive of them. If we have no 
ear for music, we cannot realize what it is, and so we can 
hardly help thinking that the enjoyment which others profess 
to get out of it is largely affected; if we have never been on 
the edge of nervous prostration, we are likely to believe that 
the utter exhaustion which others sometimes say they feel is 
merely ' imagination ' or an empty excuse for laziness; if we 
have never suffered great pain, we are inclined to think that 
it cannot be so very terrible; and if we have never done a 
generous deed or sacrificed ourselves for a principle, we are 
likely to find nothing in stories of such devotion but veiled 
selfishness and hypocrisy. We cannot realize what these 
things mean, and so we do not believe in them. 

What is true of these simple feelings and motives is true 
also of things and situations that are more complex. We 
sometimes read in books on psychology that if we have a 
3eparate knowledge of each of the elements that enter into 



412 THE THREE ULTIMATE TESTS OF TRUTH. 

some situation, we can put them all together and thus 
imagine the situation as a whole. But this is no easy 
matter. We may know the meaning of every word in a 
description, but unless the thing described bears some total 
resemblance to something with which we are familiar it is 
extremely difficult to conceive of the separate details at once 
and hold them together in such a way as to get anything 
like a reliable conception of the whole. Experience begins 
with wholes and not with parts; and it is a great deal easier 
to construct a new whole by modifying an old one something 
like it than by laboriously fitting and holding together a 
large number of details. Indeed this is the way we almost 
always proceed. And from this it follows that the more 
total resemblance a new thing is supposed to bear to some- 
thing with which we are familiar the easier it is to conceive 
of it, and the less total resemblance it is supposed to bear 
to anything with which we are familiar the harder it is to 
conceive of it.* And when it comes to a question of what 
we shall believe, the relatively familiar conception is likely 

* This of course is the psychological law of apperception, and it ex- 
plains the old rule that definition should be by genus and difference 
rather than by an enumeration of all the generic qualities as well as the 
specific in detail. 

Complexity and novelty produce a certain inconceivability, but it is 
relative, and must be distinguished very sharply from the absolute incon- 
ceivability that was discussed a few pages back. Even when relations 
are so very complex that we feel sure no human mind could possibly 
picture them all together {e.g.^ the position of every atom in an ink- 
bottle), nobody believes that this kind of inconceivability proves the 
relations to be impossible. Because we cannot think of a great many 
things at the same time we never think of denying that they can exist 
together. We recognize that the discrepancy is due to our own weak- 
ness ; to a certain fluidity of mind which makes it impossible to hold 
more than a few relations steadily before us at once. The kind of in- 
conceivability that we discussed before seems, on the other hand, to be 
due rather to a certain mental firmness or rigidity : the relations keep 
their place quite steadily; and somehow we cannot make them bend to 
fit each Qth^r, 



ANALOGY. 413 

to be present and available when the less familiar has become 
too vague and shadowy to be taken hold of. 

Thus the more some new state of affairs resembles one to 
which we are accustomed the easier it is to believe in it, if 
for no other reason, merely because it is easier to conceive 
of it. 

When two things or situations resemble each other closely 
as a whole as well as in many of their details, there is a fair 
presumption that they resemble each other also 
in some other detail. The close resemblance 
between Mars and the earth in many known respects makes 
it more or less probable that Mars resembles the earth also 
in being inhabited ; and the close resemblance between the 
lower animals and man in a multitude of other respects 
makes it probable that those animals resemble man also in 
possessing consciousness. Arguments of this sort are said 
to be * from Analogy '. Such arguments are never absolutely 
conclusive. 

In general, the larger the proportion of respects in which 
the things compared are known to resemble each other and 
the stronger the resemblance in each, the stronger is the 
argument. But where the matter in question is known to 
be specially connected with some known point of resem- 
blance or difference, general resemblance or difference does 
not count for so much. However much the moon may be 
like the earth in other respects, the one fact that it has no 
atmosphere is proof positive that it has no inhabitants like 
ourselves. 

Many so-called arguments from analogy are little more 
than metaphors, and quite worthless as arguments: e.g., the 
argument that a mother country has a right to regulate the 
internal affairs of a colony because a mother has a right to 
absolute control over her young daughter; or the argument 
that parliamentary government is always bound to fail 
because Victories may be won by a poor general, but never 
by a debating society \ 



414 THE THREE ULTIMATE TESTS OF TRUTH. 

Any decidedly new idea may be rejected as / absurd ' ; but 
when it is not merely new but also contrary to our accus- 
tomed modes of thought the rejection is more 
Absurdity. , • i , 

emphatic and the term seems more appropriate. 

To believe in something that is merely different from what 
we have been accustomed to requires that we shall form 
a new habit of thought; to believe in something directly 
opposed to what we are accustomed to requires that we 
shall break up an old one, and for people old enough to 
have fixed habits this is often much more difficult. We are 
inclined to object to it in precisely the same way as we 
might object to having our things put away in some new 
place, or wearing skirts instead of trousers, or living under a 
new kind of government, or leaving old friends and associat- 
ing with old enemies. The new arrangement seems intrinsi- 
cally bad, but in reality the badness lies only in its relation 
to us. It is bad merely because it is new, and a person 
accustomed to it would find ours just as bad. So it is with 
beliefs. Apart from contradictions there is no such thing 
as an idea which is absurd in itself, and when we reject a 
new view as absurd it is not because our reason sees the 
absurdity; on the contrary, it seems absurd because our 
habits compel us to reject it. Thus we use Absurdity as a 
test of truth, not because we have concluded beforehand 
that the test is reasonable, but merely because we are 
creatures of habit and cannot help it. 

Often the absurdity of a new view appears not so much in 
the bare outline as in the details. We try to think them all 
out according to the new idea, but we keep putting in the 
old ones until at last we gQt a hopeless confusion of the new 
and the old, and then we say. See how inconsistent and 
ridiculous this new view is ! Thus when Columbus suggested 
that there might be land on the other side of the world as a 
kind of counterpoise to Europe, his critics replied that that 
was impossible; for if there were land there, the inhabitants 
would have to walk upon their heads (since their feet would 



ABSURDITY. 415 

be up, towards the sky above Europe, and their heads would 
be down). This filling out of the details according to old 
habits is often almost as true of those who embrace the new 
idea as of those who reject it. The new doctrine may fill 
them with a grand enthusiasm ; but when it comes to work- 
ing out the details the old ideas keep coming back to give 
the new words their meaning: 'New Presbyter is but old 
Priest writ large ', and a revolution of any sort retains vastly 
more of the past than those who are in it realize,"^ 

Because the impression of Absurdity (as distinguished 
from contradiction and true inconceivability) depends upon 
a breach with established ways of thinking rather than upon 
any intrinsic imperfection in the idea itself, there is hardly 
an idea which has not seemed absurd to somebody at some 
time. The King of Siam in the traveller's story refused to 
believe the absurd tale that water sometimes got solid; to 
Aristotle it was absurd to suppose that slavery should cease 
to exist, or looms work without hands; and so with others 
it seemed absurd to suppose that the tradition of the elders 
might be superseded; that a good thing could come out of 
Nazareth; that a man should love his enemy; that a law- 
observing Pharisee might be no better at heart than a law- 
breaking publican; that the earth moves; that a man might 
rightly disobey the king; that there are no ghosts or 
witches; that slavery is not a divine institution; that men 
and monkeys had the same ancestors; that steam could be 
made to do w^ork; that it is possible to travel sixty or eighty 
miles an hour, talk with people hundreds of miles away, see 
through solid boards, or read at your breakfast-table in 
America what they did in Europe on the same day at noon. 

These examples show how unreliable the test of absurdity 
is ; and yet, in spite of its unreliability, we should be abso- 
lutely helpless without it : the victims of every passing sug- 

* This explains, too, the many ' rebukes ' that Jesus had to give his 
disciples. Again and again the old ways of thinking would return and 
they had to be told, "Ye know not what manner of spirit ye are of." 



4i6 THE THREE ULTIMATE TESTS OF TRUTH. 

gestion, utterly devoid of all stability of thought or purpose 
and absolutely incapable of anything like steady progress. 

Just as novelty gives the impression of absurdity, so famili- 
arity removes it. Repeat a suggestion or a statement often 
enough and the sense of incongruity gradually wears away 
and the mind at last becomes ' open 'to it. In this way mere 
habituation — the mere continued effort to see things from 
the new standpoint — often does more to produce conviction 
than argument. With such a thing, for example, as James's 
doctrine that the bodily ' expression ' of an emotion deter- 
mines the feeling, and not vice versa, students may think they 
see how much force there is in the argument at once, but 
they really do not /eel its force until after they get used to 
the conception. When they have learned to find their way 
around in it they may accept it genuinely, but not before. 

Sometimes it is possible to remove the sense of absurdity 
from a conception almost instantly by showing that thougli it 
seems strange it is really very much like some other to which 
we are accustomed. That the Roentgen rays should pene- 
trate solid boards seems very marvellous, and had the facts 
been less well authenticated those who heard the story when 
it was new might well have said it was much too absurd to 
be true ; but when we are reminded that common light-waves 
pass through glass as thick and solid as the boards, it is easier 
to believe the story of the Roentgen rays. 

When two explanations are equally good in other respects 

we tend to choose the simpler, and we feel that 
Simplicity. , , , ,....»,, 

somehow or other the choice is justifiable. 

We tend to believe in a simple state of affairs rather than 

a complex, just as we tend to believe in a familiar rather than 

an unfamiliar — for one thing — merely because the former is 

clearly remembered when the occasion for explanation arises, 

while the latter is confused or forgotten. This is one reason. 

But then, again, even when two explanations are conceived 

with equal clearness and equally well remembered we cannot 

help regarding the simpler one as ' better ', All explanation 



SIMPLICITY. 417 

is an attempt to find uniformity behind apparent disorder or 
anomalies, and the simpler the total state of affairs which we 
suppose to be there the more apparent and striking is the 
uniformity. A simple explanation is always more ' beauti- 
ful ' than a complex. Then, again, in the third place, we 
ourselves, as creatures of limited time and strength, are 
always accustomed to accomplish our own ends by the sim- 
plest means possible and to see others do the same. Sim- 
plicity of means thus becomes a very practical ideal which 
we seek both to realize and to find in all human affairs ; and 
when we come to deal with Nature the force of habit carries 
us on to seek for it there also, as though we knew beforehand 
that Nature were the product of some intelligent being work- 
ing for ends like ours according to our ideals. Leibnitz 
says : ^^True physics must be derived really from the source 
of the divine perfections. It is God who is the final reason 
of things, and the knowledge of God is no less the principle 
of the sciences than his essence and his will are the principles 
of beings. The most reasonable philosophers agree to this, 
but there are very few of them who can make use of it to 
discover truths of importance. . . . Far from excluding _^;/ (2/ 
causes and the consideration of a being acting with wisdom, 
it is from thence that all must be derived in physics." * 

I do not think that one needs to know about God or to 
believe in him in order to seek for ends and simplicity and 
other forms of rationality in Nature ; but rather, on the con- 
trary, that it is because we cannot help seeking for these that 
we do believe in him. 

The rule of simplicity in explanation was laid down as a 
formal principle by the Franciscan monk William of Occam, 
in these words : Entia non sunt viuliiplicanda prceter necessi- 
iatem,\ This is known as Occam's Razor, or the Law of 

* Letter to Bayle, 1687. Duncan's " Philosophical Works of Leibnitz ", 

PP- 35, 36. 

f ' We must not assume the existence of any more things than neces- 
sary.' Occam died in 1347. Petrus Areolus, another Franciscan, who 



4i8 THE thre:e ultimate tests of truth. 

Parsimony. He used the razor to good effect to get rid of 
the abstractions which the recognized philosophy of his time 
took for things.* But nowadays, when explanations are 
concerned quite as much with the laws of action as with the 
things that are supposed to act, we may interpret the princi- 
ple to mean not merely that the things we assume to exist or 
to be present mast not be more numerous than necessary, 
but also that the laws must not be more complex. The 
thinors we assumed would be unnecessarily numerous if we 
supposed that God created the world through the efforts of 
a dozen different grades of inferior spirits, when all the facts 
would be explained just as well on the assumption that he 
did it all himself. The laws we assumed would be unneces- 
sarily complex if we supposed that the planets moved in 
cycles and epicycles instead of in simple ellipses, or that 
elements did not combine chemically in simple proportions, 
but according to some very complex law that led to the same 
practical results. 

When we try to make every explanation as simple as pos- 
sible we are confronted by several dangers. The first of these 
is that we shall find simplicity by ignoring some essential part 
of the facts we are trying to explain. The theory that every 
vokmtary act is done for the sake of gaining pleasure or avoid- 
ing pain is extremely simple and it can be made to explain a 
great many facts of conduct; but it certainly ignores the things 
that people sometimes do, knowing all the time that they 
will lead in the end to far more pain than pleasure. The 
theory that fear is due to a perception of danger will explain 
a great deal ; but it cannot explain why children often sud- 
denly and spontaneously begin to be afraid of things that 
have never hurt them, or why many adults show inordinate 

died in 1321, had said the same thing in these words : Non est philoso- 
phicufn^ phtralitatem rerum ponere si7ie causa ; frtistra enim fit per 
plura quod fieri potest per pauciora. 

'^ ' ' Siifficiunt singularia, et ita tales res tiniversalia onmino frustra 
ponmitur," 



SIMPLICITY. 419 

fear of such things as cats, mice, caterpillars, and common 
snakes, whi(^h they know perfectly well to be harmless. 
Thus the alleged explanation is too simple; for it ignores an 
important part of the facts to be explained. 

The second danger is that of attaining simplicity in explana- 
tion by ignoring the relations of the facts we are trying to 
explain to the rest of the world. The ideal of all science and 
philosophy is the simplest possible connected view of the 
whole universe; but in trying to attain it we must not be 
penny wise and pound foolish. There is a difference, as 
Kipling says, between a team of good players and a good 
team of players ; and there is a difference betw^een a set of 
good explanations and a good set of explanations. A simple 
explanation of some one little fact that w^ill not fit in with 
our explanations of the rest of the world is not so satisfactory 
as a more complicated explanation that will. Suppose, for 
example, that the old witchcraft and demon ology or that the 
modern telepathy and spiritualism gave or could be made to 
give a perfectly simple, coherent, and well-articulated expla- 
nation of the particular set of facts w-ith which they deal. The 
explanation given would be extremely unsatisfactory, and 
would doubtless be rejected by many scientists as w^holly unsci- 
entific, so long as there w^as no way of fitting the telepathic and 
spiritualistic conception of things in wdth the vast and ever- 
growing mass of facts that are being continually explained 
and coordinated more and more closely every day from other 
points of view. If the facts that the telepathists and spirit- 
ualists deal with can be explained piecemeal by principles 
recognized elsewhere, no scientist doubts that such an ex- 
planation is far better than one by thought-transference and 
spirits, although the latter might be a great deal simpler so 
far as the one set of facts was concerned. 

It was some such feeling as this of opposition to the intro- 
duction of totally new principles of explanation serviceable in 
only one special field that Newton expressed in his celebrated 
dictum : Hypotheses 7ion jingo. The cause which we assign 



420 THE THREE ULTIMATE TESTS OF TRUTH. 

for any known effect must be, he said, vera causa: a true 
cause, or one for whose existence we have more evidence than 
can be found in the special facts that it is invoked to explain. 
A third danger connected with the principle of simplicity 
is the opposite of that just explained. It is undoubtedly 
true that a complicated explanation of the facts in some one 
field, that fits in with what we know about all the rest of the 
world, is better than a simple explanation that does not, and 
it is just as true that we must not accept the new set of causes 
until we have made a reasonable effort to explain the various 
facts in question by old ones; and yet, on the other hand, we 
must not carry our rejection of strange causes to an extreme. 
If the alleged new principle does nothing else, it may serve to 
hold together a mass of facts many of which would otherwise 
escape us or become hopelessly confused, and to keep us 
puzzled until we find some other explanation that is better. 
In this way even a false hypothesis is often better than none 
at all. And then, again, it may turn out that our discon- 
nected principle is not false after all. It is true that our sci- 
entific ideal is a simple, well-coordinated view of the world 
as a whole; but it is also true that we are a long way from 
attaining it. What we possess in the way of knowledge is 
not so much one field that is always growing broader as a 
large number of fields each of which is growing out towards 
the others so that sometimes they meet ; but there are still 
plenty of gaps, and we m^ust not always refuse to cultivate 
some new field because we do not see how it can be joined 
with the rest. It is nearly as bad to try to make our differ- 
ent hypotheses consistent with each other too soon as not to 
try to do so at all. The Greek philosophers except Aristotle 
were always thinking about the sum-total of things,^ and 
Aristotle is the only one of them who made anything like a 
respectable contribution to science. Descartes was thinking 
about the ultimate relations of mind and matt<^r, and his gen- 
eral standpoint compelled him to say that the lower animals 
were mere automata : mechanical toys that cried when you 



THE RIGHT TO ASSUME THESE PRINCIPLES. 42 1 

kicked them, just as a bell rings when you shake it, without 
any feeling whatever. 

Thus the Principle of Simplicity or Parsimony is one that 
we are compelled to follow, but often it is hard to tell whether 
we will not reach it sooner in the end by leaving it for the 
moment. 

Of course it is one thing to be so organized that the sim- 
ple and familiar are more easily believed in than the compli- 
cated and unfamiliar, and a somewhat different 
1 . 1 r 1 • • 1 1 1 The rigflit to 

thnig to accept the formal prmciple that where assume these 

there are two theories, equally good in other re- ^ "^ 
spects, that which assumes the simpler and more familiar state 
of affairs is the more likely to be true. And yet if we have 
the organization, we can hardly avoid the principle. To say 
that the simpler and more familiar is more easily believed 
in means that in most cases we do believe in it, or, in 
other words, that in most cases the relatively simple and 
familiar state of affairs is what we call the 'true ' one ; and 
now, a large number of particular cases being settled, all we 
have to do is to compare them and we reach our formal prin- 
ciple : The theory which supposes the simpler and more 
familiar state of affairs is more often true than the other. ^ 

It IS because we act on this principle of discrediting the 
new, whether we ever state it in words or not, that the phrase 
^ a very strange story ' generally means a lie. 

So much for the fact that we actually do use Consistency, 
Conceivability, and Uniformity and Simplicity as tests of 
truth, and even for the further fact that we come to think we 
have a right to. But have we this right? Is it possible to 
prove that there is such a relation in the world as com- 

•5f We get the principle when we reflect enough to see the results of 
our own organization [i.e.^ to see that all our explanations are rela- 
tively simple) but not enough to see that they are the results of that 
organization {i.e,^ that these explanations are simple because the sim- 
ple ones are those we chose). When we see that the question takes a 
new form. 



42 2 THE THREE ULTIMATE TESTS OF TRUTH. 

patibility or incompatibility? Can we prove that anything 
real conforms or ought to conform to the laws of our imagi- 
nation ? Hardest of all, can we prove that because some- 
thing is uniform or simple and therefore easy for us to think 
of, it is any easier on that account for it to exist? And if 
we cannot prove these things, have we any real right to use 
the tests? My answer so far as uniformity is concerned has 
been given already in Chapter XXII. I believe that we 
cannot prove these thiAgs, and therefore cannot prove our 
right to use the tests. We simply take them for granted and 
take the right to use the tests for granted along with them. 

The time has gone by long since when wise men sought 
for a philosophy without assumptions ; and if we cannot get 
along without them in philosophy, we certainly cannot get 
along without them in common life and m the logic that tries 
to serve as a guide for common life. If any one believes, as 
Kant did, that not only colors and sounds and smells and 
tastes, but also Space and Time with all their relations of 
shape, size, distance, direction, duration, coexistence, and 
succession, are purely human ways of imagining things and 
do not really belong to things in themselves at all, then that 
person ought not to use conceivability as a test of what things 
in themselves can or cannot be. If any one has meditated 
about these topics so long that it no longer seems to him 
absurd to doubt the simplicity and general rationality of 
Nature, I do not see how it is possible to restore his faith by 
demonstration ; and if he has emancipated himself from the 
bonds of habit so completely that he really doubts the ex- 
istence of those principles of uniformity that we indicate by 
the words Thing and Kind and Cause and Law, then there is 
certainly no way of proving to him that one explanation is 
better than another, or indeed that anything needs explana- 
tion at all. If, finally, he really and truly doubts — as Des- 
cartes tried to — the existence of everything but his own pass- 
ing thought, I do not see how we could prove to his satis- 
faction that there is a real nature of things in virtue of 



THE LliMITS OF I'ROOF. ^ 423 

which one supposed fact is incompatible with another, and 
therefore that there really is such a thing as a contradiction. 

If people actually doubt all these things, we do not argue 
with them : we lock them up instead, and by this resort to 
brute force we confess defeat in the field of pure argument. 
If, on the other hand, they profess to doubt them, but show by 
their acts or their argument — perhaps by the very fact of talk- 
ing with us — that when they are off their guard they really take 
them for granted, the most we can do is to point out the incon- 
sistency, with the hope that their faith in law and a nature 
of things is so strong at bottom that inconsistency in an 
argument will seem to them a fault. We cannot go beyond 
this appeal to faith. Thus we start with faith in experience 
as a whole, however vaguely we may conceive of this experi- 
ence ; but such a faith implies also faith in all the ultiinate 
principles that that experience involves. 

There are some questions which logic and its tests of truth 
will never help us to settle. If it is a question whether a 
certain state of affairs exists, and if there is no 
objection so far as consistency and conceivability ofproS^.^^ 
are concerned to believing that it does, the only 
way of settling the question is to ask whether any one has 
observed the state of affairs itself or anything that can be 
recognized as its necessary cause or effect. If we cannot 
observe the state of affairs itself and if we cannot prove that 
anything which we do observe must be connected causally 
with something of the sort, we cannot prove that it exists. 
But if the state of affairs in question is one that might exist 
without being observed or producing unmistakable effects, we 
cannot prove either that it does not exist. It may be that 
there are mountains on the other side of the moon ; but we 
cannot see them, and we do not know of any change that 
they would make in what we do see if they were there ; con- 
sequently we cannot tell whether they are there or not. It 
may be that plants feel, that they enjoy the sunlight and 
the rain and suffer discomfort in the cold ; but feelings can 



424 THE THREE ULTIMATE TESTS OF TRUTH. 

never be perceived directly except in ourselves, and we have 
no idea what change their presence or their absence would 
make in the behavior of a plant, and so we can never know 
whether plants have them or not. It may be that every 
living soul existed on the earth before in the body of some man 
or beast although it has forgotten what took place in its life 
there ; but no one knows how the life of a reincarnated soul 
should differ from that of one that never lived before, and so 
no one can ever tell from what he observes whether the theory 
of transmigration is true or not. It may be, finally, that the 
world was created in infinite love and wisdom and that all 
our human experiences are intended as preparations for some 
glorified life after death ; but no one knows enough about 
infinite love and wisdom to say how a world made by it 
would differ from any other world, or how a life intended by 
the Creator as a preparation for another would differ from 
one which was not ; and therefore nothing that we observe 
in the world can prove the matter one way or the other. 

What we believe about questions like these is not inferred 
by logical processes from what we observe in the world; but 
is added to what we observe, as a matter of religious faith. 
Such a faith gives our experiences a new kind of significance ; 
but no particular experience of the sort that science deals 
with can either confirm or refute that faith ; and this is why 
different people often give diametrically opposite religious 
interpretations to the same concrete experiences. 

It often seems indeed to persons of a certain temperament 
or character that some observable fact is a sufficient proof of 
what they believe about religion ; and perhaps they make 
long abstract arguments to show it ; but abstract arguments 
are hard to criticise in any case, and it requires an unusual 
amount of intellectual honesty and energy to seek for obscure 
fallacies in arguments that profess to prove what we already 
believe or wish to believe ; and so this appearance of logical 
proof is easy enough to account for. 

There is only one way in which logic or a knowledge of 



THE LIMITS OF PROOF. 4^5 

scientific method can help us in matters of this kind. It can 
show us its own limitations, and save us in this way, on the 
one hand, from the trouble of constructing long and labored 
arguments that do not prove anything, and, on the other, from 
the error of supposing that the absence of proof in favor of 
certain beliefs can be taken as any argument against them. 

Science and faith, particularly religious faith, are often 
supposed to be in some kind of logical conflict with each 
other. But this is a mistake. Science itself rests on faith, 
for it assumes, as we have seen, that there is such a thing as 
a world beyond one's own individual sensations, and that 
that world really possesses the uniformity and coherence 
which we feel impelled, as creatures of habit, to read into it. 
Indeed what we call scientific ^ knowledge' is simply an in- 
terpretation that we give to our experience or some of it on 
the basis of this faith. But a faith in uniformity and coher- 
ence is certainly not inconsistent with a faith in purpose and 
wisdom and goodness also, and the mere fact that science 
does not attempt to unify experience from the standpoint of 
this latter faith as well as from that of the former is no rea- 
son why the scientist should not do so when he leaves his 
science and begins to think of something else. Religion 
cannot tell what the world looks like, and science cannot tell 
anything about its spiritual values ; but for this very reason 
the one is no more inconsistent with the other than geom- 
etry or psychology is inconsistent with aesthetics or juris- 
prudence. 



NOTE. 

Some of the following examples for which no credit is 
given are used in many different books, and I have not taken 
the trouble to trace their origin. The initials after others 
should be interpreted as follows: 

C, for J. E. Creighton's '' Introductory Logic''; 

D, for N. K. Davis's '' Theory of Thought "; 

F, for Thomas Fowler's " Elements of Deductive Logic " ; 
H, for J. H. Hyslop's '' Elements of Logic "; 
J, for W. S. Jevons's *' Elementary Lessons in Logic ", or 
his '' Studies in Deductive Logic "; 

W, for Archbishop Whately's ** Elements of Logic ". 

426 



EXERCISES. 

With every chapter students are advised to make use of the 
marginal summaries or the table of contents to assist them in 
review, thus : What are the two kinds of thinking? What is 
the nature of judgments and propositions, and how are they 
related to each other ? 



CHAPTER I. 

I. Estimate the value of the following arguments: 

{a) Tolstoi's interpretation of Christianity must be false ; for 
if it is correct we and our ancestors have not been Christians 
at all. 

{b) You may have an ape for an ancestor if you want to ; but 
I don't care for one. 

{c) " To believe that man was aboriginally civilized and then 
suffered utter degradation in so many regions, is to take a pitia- 
bly low view of human nature. It is apparently a truer and 
more cheerful view that progress has been much more general 
than retrogression ; that man has risen, though by slow and 
interrupted steps, -from a lowly condition to the highest stand- 
ard as yet attained by him in knowledge, morals, and religion." 
(Darwin's ''Descent of Man ", end of Chap. V.) 

(d ) Of course you ought to be good, for you belong to a 
church and go to prayer-meeting; but I make no professions. 

(6') If he thinks it is wnmg, it is wrong for him ; but w^ith me 
the case is very different, for I never thought it was wrong. 

(/) It is all very well for you to talk; but if these ideals of 
yours are so very beautiful, why don't you put them into 
practice ? 

(^) * Is there a hell ? ' — That depends altogether upon your 
point of view, 

427 



42 8 EXERCISES. 

iji) " But if there be no resurrection from the dead, then is 
Christ not risen ; and if Christ be not risen, then is our preach- 
ing vain and your faith is also vain." (I. Cor. xv. 13, 14.) 

(/) You say that ' of ' is a preposition, but that cannot be ; for 
in the very sentence in which you say so it is a noun. 

(7) ' We know what we mean by clear water or a clear atmos- 
phere, then why shouldn't we know what we mean by clear 
ideas .^' *I suppose you mean that a hazy atmosphere is one 
that you can see and that a clear atmosphere is one that you 
can not see, and that in the same way the clearest ideas are the 
only ones that we can not see.' 

{k) Charlemagne is king ; king is four letters ; therefore 
Charlemagne is four letters. 

(/) I cannot accept your opinion as true, for it seems to me 
that its general recognition would be attended with the most 
injurious consequences to society. (F.) 

2. What is the best way to persuade the slothful man that 
there is no lion in the way ? 

3. Is there any objection to the following? — ''General names 
are predicable of individuals because they possess certain attri- 
butes ; to predicate the possession of those attributes is the 
same thing as to predicate the general name." 



CHAPTER 11. 

1. What is the meaning of the word ' doubt ' in the following 
lines } — 

Doubt that the stars are fire ; 

Doubt that the sun doth move ; 
Doubt truth to be a liar ; 

But never doubt I love. 

2. Explain the following : 

The good are envied of the bad, and glory finds disdain, 
And people are in constancy as April is in rain. 

3. What is the meaning of the word 'or' in the following 
sentences.^ — 'John or James will do'; 'Sodium chloride or 
common salt is always present ' ; * Clergymen or lawyers always 
get in '. 



EXERCISES. 429 

4. What is meant by the following statements, and in what 
sense is the second of them true ? — 

(a) Our team wins every year, except in off years. 

(d) No one's burden is ever greater than he can bear. 

^a. What is meant by 'the people' in the phrase "Govern- 
ment of the people, for the people, by the people " ? 

5^. What was meant by the statement that all men are born 
free and eqiial? In what sense of the words is it true ? 

5^. In the exercises to Chapter V are two passages from 
Bacon. Find the meaning of all the words used there in an 
obsolete or peculiar sense. 

6. Define the terms * Wealth ', ' Capital ', * Society ', ' Friend ', 
* Courage ', ' House ', ' Savage ', * Nice ', ' Lady ', ' Pious ', ' Poor 
man ', ' The weak ', ' Educated ', * Circle ', ' Triangle ', ' Sopho- 
more '. Why are the last three words more easily defined than 
the others } 

7. Criticise the following arguments : 

{a) The college chapel is sacred ; for a chapel is a kind of 
church, and the Church is a divine institution. 

(b) This stove saves half the ordinary amount of fuel ; there- 
fore tw^o such stoves would save it all. 

(c) A. B. is professor of religion in the university, but as he 
is very irreligious he does not possess the religion he professes; 
he is therefore a hypocrite. 

{d') All presuming men are contemptible; this man therefore 
is contemptible, for he presumes to believe his opinions are 
correct. (J.) 

{e) It is good to be great and it is right to be good ; Napoleon 
was great ; therefore it is right to be like Napoleon. 

(/) A thoughtless person does not think; one who does not 
think cannot form a judgment; therefore a thoughtless person 
cannot form a judgment. 

(^) It is wrong to criticise an inspired book; the historians 
apply criticism to the Bible ; therefore they do wrong. 

{Ji) No evil should be allow^ed that good may come of it; all 
punishment is an evil; therefore no punishment should be 
allowed that good may come of it. 

(/) Whatever is dictated by Nature is allowable ; devoted- 
ness to the pursuit of pleasure in youth, and to that of gain 
in old age, are dictated by Nature ; therefore they are allow- 
able. (W.) 



43 o EXERCISES. 

8. A hunter is trying to shoot a squirrel that is dinging to a 
stump, and goes all around the stump to find him ; but the 
squirrel always keeps on the opposite side of the stump. Does 
the hunter go around the squirrel.^ 

9. Which hen is the mother of the chicken, the one that laid 
the tgg, or the one that hatched it out and takes care of it ? 

10. What is the true significance of the last two questions ? 

11. Analyze the following explanations, arguments, and defi- 
nitions : 

(a) These two elements almost always unite when they are 
put together, for they have an affinity for each other. 

(d) It is harder to slide on wood than on ice, because the fric- 
tion is greater. 

(c) Movement catches the attention, and therefore we are 
more likely to notice a moving object than one that remains 
stationary. 

(d) It is always wrong to lie ; for any departure, for any 
reason whatever, from the one invariable law of absolute 
veracity is always reprehensible. 

(e) An archbishop is one who discharges archiepiscopal 
functions. 

(/) Habit can be defined as * the purgatory in which we 
atone for our past misdeeds '. 

(^■) " A definition is the exposition of the connotation of a 
term." 

(//) Definition is the enumeration of the parts of an idea. 

(/) The process by which the qualities that belong to an 
object is defined is called logical definition. 

(J) *' Despite the hot weather two cases of smallpox were 
discovered yesterday. . . . The discovery of these occasional 
cases, the health authorities say, is evidence that the plague is 
still prevalent in the city." 

12. Make five arguments that turn upon ambiguous words, 
five purely verbal explanations, and five purely verbal defini- 
tions. 

13. Define all the important words in the Declaration of 
Independence or some other connected discourse. 

14. Is any fault to be found with any of the following rules 
for definition or the way in which they are stated ? — 

(a) A definition should contain the essential attributes of the 
word or object being defined. 



EXERCISES. 43^ 

{b) A definition should contain an adequate description cf 
the term defined. 

U) The subject of a definition must be exactly equivalent to 
the predicate. 

{d) A definition must not be defined by figurative or ambigu- 
ous terms : Death is an undisturbed sleep (figurative). 

(<?) The definition must be equivalent to the term defined: 
Rhubarb is a plant (which can be eaten). 

( /) A definition must state the essential qualities of the term 
defined : A classical student is one who has studied Latin 
(Greek is also essential). 

(^) Give all the essential qualities of the species to which the 
object defined belongs. 

15. Criticise the following definitions : 

(ai) A JUDGMENT is a conclusion reached after considering 
certain previous propositions upon the same subject but pre- 
senting different views. 

(a2) Judgment is the conclusion arrived at after correct, 
logical analysis of a matter. 

(^3) Judgment is estimating the relative value of things. 

(^4) Judgment is the comparison of two or more simple 
apprehensions. 

(a^) A judgment is an inference made from material gained 
by reasoning. 

(a6) Judgment is logical conclusion drawn from given hypo- 
thesis. 

(ay) Judgment is the process of clear thinking, of estimating 
accurately, and finally of reaching a decision. 

(czS) A judgment is the expression of a belief, conclusion, 
determination, and the like. 

(ag) Judgment is a statement which affirms or denies some- 
thing. 

(^10) Judgment is that act of the mind by which we deduce 
from two statements a third. 

(an) Judgment is anything which when stated will form a 
proposition. 

(ai2) Judgment is a decision as to the truth or falsity of a 
statement. 

(^i) A PROPOSITION is a phrase that expresses a thought in 
form of a subject and predicate ; a judgment, the predicate 
giving some relation, condition, or quality of the subject, 



432 EXERCISES. 

{b2) A proposition is a thought expressed in the form of a 
sentence, consisting of subject and modifiers, predicate and 
modifiers, and copula. 

(<^3) A proposition is a statement which contains a subject 
and predicate and forms a part of a syllogism. 

(^4) A proposition is an equation consisting of a subject 
term, a predicate term, and a copula. 

(ds) A proposition is a statement of a true or false fact. 

(^6) A proposition is an assertion which expresses a declara- 
tion either positive or negative. 

(^7) A proposition is a statement in the form of a gram- 
matical sentence which affirms or denies a fact. 

(^8) A proposition is a statement that asserts something. 

((^9) A proposition is a statement which must contain a sub- 
ject and predicate; in which the predicate asserts or denies or 
questions a relation existing between it and the subject. 

(^i) Subject of a proposition is that of which something is 
affirmed. 

(c2) The subject of a proposition is the word about which 
something is said ; e.^-., The dook is lying on the table. 

(<f3) The subject of a proposition is the object or objects 
about which a statement is made. 

(<r4) The subject of a proposition is that of which something 
is affirmed or denied by the verb and rest of the proposition. 

((f5) The subject of a proposition is the object of discourse. 

(c6) The subject of a proposition is the name of an object or 
substance concerning which a statement is made in the predi- 
cate term. 

(cy) The subject of a proposition is a word or group of words 
about which something is said. 

{cS) The subject of a proposition is that about which some 
statement is made. It includes the word and all of its modi- 
fiers. 

(eg) The subject of a proposition is a word, phrase, or clause 
of which something is affirmed or denied in the predicate. 



EXERCISES. 433 



CHAPTER III. 



1. Summarize the opening lines of "Paradise Lost" in the 
plainest and most concrete language possible, getting rid of all 
the figures of speech and abstract terms, but giving their mean- 
ing in the simplest prose. Make summaries also of as many 
paragraphs as possible from Berkeley's '' Principles of Human 
Knowledge", of the editorials in the morning paper, and of a 
couple of pages from some such book as Mrs. Eddy's " Science 
and Health". In making these summaries be careful to put in 
all the little connecting words, such as * and ', * or ', ' because ', 
* therefore', * in other words ', etc. ; use your own language, not 
that of the author summarized ; and take care to make your 
meaning absolutely clear and unambiguous, even if you have to 
give several alternative interpretations to a passage. 

Why is it that some of these summaries are harder to make 
than others? Is it because the subject-matter is more difficult 
or because the writer's ideas are more hazy ? 

2. Explain the meaning of the law of gravitation ; of the 
formulae on pp. 170, 175, 263, 265, 278, and 292 of this book; 
and of any other formulae that seem rather hard and complex. 

3. Determine exactly what was meant by each one of the 
Ten Commandments, and show where we might commit a 
fallacy of Accident or Accent in interpreting them. 

4. What fallacy did Bismarck commit in his abridgment of 
the Ems despatch ? and what fallacy did Columbus commit 
when he proved that an egg could stand on end ? (J.) 

5. In what sense is it true and in what sense is it false that 
" There is nothing either good or bad, but thinking makes it 
so.".^ 

6. What fallacy, if any, is to be found in the following argu- 
ments : 

(a) You say now that you never believed in the war with 
Spain, and yet you voted for it ; for you voted for the Repub- 
lican ticket when their platform had already declared in favor 
of intervention, and everybody knew that intervention meant 
war. 

(d) It is right to help the needy ; therefore it is right to give 
to this beggar, for he is needy. 



434 EXERCISES. 

{c) In going around the world westward we keep gaining 
time, and the whole trip would gain us a full day ; therefore if 
we could make the complete journey in twenty-four hours it 
would really take us no time at all 

{d) It is not true that on the first of next month John Smith 
will become the husband of Miss Brown ; he will become the 
husband of Mrs. John Smith. 

{e) No cat has nine tails ; one cat has one tail more than no 
cat ; therefore one cat has ten tails. 

(/) Keeping a promise is right; Herod kept his promise 
when he killed John the Baptist ; therefore he did right. 

{g) Peter is a saint ; therefore his denial of his Lord was the 
act of a saint. 

{h) You are not what I am ; I am a man ; therefore you are 
not a man. (J.) 

(/* ) He that says you* are an animal speaks truly ; he that 
says you are a donkey says that you are an animal ; therefore 
he speaks truly. 

{j) ''Blessed are the poor in spirit." This man is a thief 
and a liar, but he is poor in spirit ; therefore he is blessed. 

' {k) It is a well-recognized maxim that the king can do no 
wrong. Unless the maxim is false it was not wrong for the 
king to say what he did. 

(/) He who is most hungry eats most ; he who eats least is 
most hungry ; therefore he who eats least eats most. (Aldrich.) 

(;;/) Nuisances are punishable by law; a noisy dog is a nui- 
sance ; therefore a noisy dog is punishable by law. (D.) 

(;/) Haste makes waste, and waste makes want ; a man there- 
fore never loses by delay. 

{o) A brick house is cooler than a frame house ; therefore this 
house is cooler than that one. 

{p) Whatever restricts liberty is bad ; government restricts 
liberty ; therefore government is bad. 

{g) Interference with another man's business is illegal ; under- 
selling interferes with another's business ; therefore underselling 
is illegal. (D.) 

7. Criticise the following definitions : 

{a) Equivocation is the use of the same word in two 
different senses in a syllogism. 

{b\) A FALLACY OF ACCIDENT occurs when a conclusion 
about a special object is drawn from a general premise, 



EXERCISES. 435 

(b2) From a general to a special case. 

(^3) The fallacy of accident is drawing a conclusion concern- 
ing the species from propositions concerning the genus. 

(^4) Fallacy of accident is when in an argument you go from 
a general rule to a special case. 



CHAPTER IV. 

1. Criticise the following divisions : 

(a) Human beings into men, women, negroes, boys, females, 
and cranks. 

{b) Religions into true and false. (C.) 

{c) Animals into bipeds, quadrupeds, birds, monkeys, and 
crawly things. 

{a) Quadrilateral figures into squares, rectangles, parallelo- 
grams, and rhomboids. (F.) 

{e) The fine arts into painting, drawing, sculpture, architec- 
ture, poetry, and photography. (F.) 

(/■) Governments into monarchies, tyrannies, oligarchies, and 
democracies. (F.) 

{g) The sciences into physical, social, ethical, logical, and 
metaphysical. (F.) 

{h) Men into fools and knaves. 

(/) Skin-diseases into those that are cured by zinc ointment 
and those that are not. 

2. " The following were the classes of persons which were in 
1868 qualified to vote in one or other of the United States of 
America : Male citizen, male inhabitant, every man, white male 
citizen, white freeman, male person, white male adult, free white 
male citizen, free white man. Form a scheme of logical division 
which shall have a place for each of the above classes." (Jevons' 
"Studies in Deductive Logic".) 

3. Criticise the following definitions : 

{ai) Genus is a class or group which contains all the funda- 
mental qualities which are necessarily possessed by the species 
in order to make it one of a certain genus. 

{a2) A genus is a class of objects made up of a collection 
of other classes, these objects being in their separate classes 
because of common characteristics. 

(^3) Genus is a class of higher objects. 



43^ EXERCISM 

(^4) Genus is a class made up of several specific classes. 

(^5) A genus is a name applied to a number of things made 
up of several (two or more) species. 

ia6) Genus is a classification of objects which can be divided 
into species. It is the largest division of objects. 

(ay) Genus is the name of a class of objects which may be 
divided into species and subdivided. 

(aS) Genus is a name of a class of objects which contain two 
or more species. 

{ag) Everything is a species of some larger class genus. Thus 
genus is class made up of smaller class species. 

(di) SUMMUM GENUS is the largest division possible of a cer- 
tain class of objects. 

(^2) Summum genus is the greatest of all genuses in exten- 
sion. 

(^3) By summum genus is meant highest division which 
can be made according to any given basis. For instance, on a 
basis of intelligence, man is the summum genus of living beings. 

(/?4) Bysummum genus ismeant the highest division, i.e., the 
division which embraces the greatest number of divisions which 
may be subdivided, e.^., Animal. 

(^5) Summum genus or genus generalissimum is the higher 
class or division which is divided into species. 

(^i) Differentiae are the attributes of the individual and 
not common to the class. 

{c2) Differentiae are fundamenta divisionis. 

{c2,) Differentiae are the attributes by which objects or classes 
of objects are distinguished from each other. 

(<r4) Differentiae are the attributes by which one genus differs 
from another. 

(c^) Differentiae is the thing upon which depends the putting 
or leaving out an object from a class. 

(c6) Differentiae are differences which objects of a certain 
class have from, each other. 

(cy) Differentiae is the name given to the difference found in 
the attributes. 

(<f8) The differentiae of a word or object express the difference 
between the object and the class to which it belongs. 

(6-9) Differentiae is the name of the attributes in virtue of 
which a species is subdivided. 

(^10) Differentiae are the attributes which must be known to 



ExmicisiEs. 437 

distinguish one species from another which belongs to the same 
genus. 

(cii) Differentiae distinguish the species of the genus. 

{ci2) Differentiae are the terms by which one object is dis- 
tinguished from another. 

(di) Accident is that quality which distinguishes one genus 
from another. 

(d2) Accident is a quality which belongs to the class genus, 
but may also belong to some other class. 

(d^) Accident is a quality which certain terms have and cer- 
tain other terms do not. 

(<^4) Accident is a property which a thing may or may not 
have and does not affect the class to which the thing belongs. 

(d^) An accident may be found in one species of a class but 
not necessarily in the others. 

(d6) Accident is that which may be true of one object of a 
class, and not true of the other objects of that class, and is not 
needed to define that object. 

(dy) An accident is a quality which belongs to an object per- 
manent or temporary. 

(^8) An accident is a relation which belongs to an object 
temporarily or which may belong to that particular object on 
account of circumstances. 

(dg) An accident is an attribute which mayor may not belong 
to individual members of the same species. 

(ei) Property is a term applied to the qualities denoted by 
the term. 

{e2) Property is a quality which is found in every species of a 
genus. 

(^3) Property consists of the quality or qualities which nmst 
be added to the species to make it a genus. 

(^4) Property is a quality that belongs to a genus, but not 
one for which the genus is especially known. 

((?5) A property of a word is one of its qualities. 

{e6) Property is a quality or qualities which an individual 
must possess in order to be distmguished from any other indi- 
vidual. 

(^7) A property of a term is something that belongs to it but 
must not necessarily be included in the definition. 

(^8) Property is a quality that belongs to every member of a 
class. 



43 8 EXERCISES. 

(eg) Property is a quality which a class of objects may possess, 
but which does not need to be defined. 

(^lo) Property is something which is true of an object, but 
which does not define that object. 

(ei i) Property of a genus or species is a quality that belongs 
to that genus or species alone and distinguishes it from all 
other genera and species. 

(/i) A CROSS-DIVISION is the classification of a term into its 
genus and species. 

(/2) Cross-division is where the word may belong to more 
than one species at once and these different species cross each 
other and make it difficult to get any good order out of them. 

(y"3) In making a division of a class of things or genus into 
species, if one of these species is made to include another there 
is a cross-division. 

(/4) Cross-division is analysis from a general term to a spe- 
cific, and from that specific used as a general term to its specific, 
until the last real specific can be found, but by not, in one or 
more cases, taking the next specific nearest to the general term. 

(/5) Division consists in placing diff'erent things into classes 
on some one basis of division. Cross-division occurs when 
division is made on two or more bases. 



CHAPTER V. 

1. Consider each of the following words as it occurs on page 
217 and determine whether it is a term or not, demonstrative or 
descriptive, connotative or non-connotative, singular or general, 
collective or distributive, abstract or concrete, positive or nega- 
tive, relative or absolute : 

Taxes, Supporting, The church. Party, Fact, The forgotten 
man, Woman, Five, Letters, Corset-stitchers, Seventy-five cents, 
Machine, Grade, Prohibitory, As, To, All, Time, Labor, En- 
hancement, Price, The tax. Best terms, Art, Commerce, To- 
day. 

2. Criticise the following definitions : 

(ai) A TERM is a word or group of words that denote a quan- 
tity, state, action, or relation of an object or class of objects 
about which something is affirmed or denied. 

(<22) Term is the name of an object or group of objects, the 



EXERCISES. 439 

quality or action or condition of the object about which we are 
thinking. 

(a2)) A term is the name of an object or group of objects de- 
noting a quality, state, action, relation, or condition about which 
we are talking or tliinking. 

(<^4) A term is the name of the quality, of the thought of the 
relation of the thing about which we are talking. 

(^5) A term is the name of an object or a group of objects 
about which something is affirmed or denied. 

{a6) A term is the name of a state, condition, or relation 
which is affirmed or denied of an object. 

{aj) A term is the name of a quality, relation, or state under 
discussion. In a proposition the subject and predicate form the 
two terms. 

(rt8) A term is a name of an object about which we are think- 
ing, asserting, or questioning some relation, quality, or con- 
dition. 

(^i) A GENERAL TERM is One that applies to all the objects 
belonging to the class to which the term applies, 

(^2) A general term is one in which all the objects included 
under a given general name are designated. 

(^3) A general term is one applicable to each of a certain 
number of similar things. 

{b/[) A general term is one which distinguishes a particular 
class of individuals as such. 

(^5) A general term is one which can be applied to any one 
of a number of specified individuals. 

{b6) A general term is one expressing all the individuals as 
such. 

{by) A general term is one which does not designate an aggre- 
gate of similar and separable things considered as a temporary 
unit. 

{bK} A general term is one denoting as such the kind of 
objects. 

(<^9) A general term is one used to designate a class of objects 
which are not separable. 

(^10) A general term is one which designates all of a class or 
group of objects. 

(ci) A SINGULAR TERM is One which has but one signification. 

{c2) A singular term is one used to apply to any one of a class 
of objects. 



440 EXERCISES. 

(^^3) A singular term is one which points to one specified ob- 
ject or class of objects. 

{c4) A singular term is a name apphed to one object to distin- 
guish it from the other objects of its class. 

(^5) A singular term is one which is applied to a single indi- 
vidual as such. 

{c6) A singular term is one which is applied to a singular in- 
dividual as such. 

(^y) A singular term concerns a particular individual as 
such. 

(cS) A singular term is one expressing a specified individual 
as such. 

(eg) A singular term is one which is applied to a particular 
designated individual. 

(cio) A singular term is the name applied to a certain desig- 
nated object. 

(^11) A singular term is a name applied to a certain distin- 
guished object. 

(ci2) Singular term is applied purely arbitrary to individuals. 

(<fi3) A singular term is one which is applied to a certain des- 
ignated object and no other in the same sense. *' This man is 
tall." Man is a singular term. 

(^14) A singular term is one which applies to only one indi- 
vidual or object. 

(di) A COLLECTIVE TERM is a term made up of individuals 
thought of as separate independent objects. 

(di) A collective term represents a number of singular units 
taken as a whole. 

(d^) A collective term is a term applied to a number of sim- 
ilar units, as in case of a mob. 

(d4) A collective term is a term applied to a group of indi- 
viduals. 

(^/5) A collective term is one in which a class of objects taken 
as a whole is designated. 

(dS) A collective term is one applicable to a whole class taken 
together. 

{dy) What is said of a collective term is said of all the objects 
comprised in the term taken as a whole. 

(^8) A collective term is one which may be applied to a num- 
ber of objects taken as a whole on the ground of some common 
likeness. 



EXERCISES. 441 

(dg) A collective term is one which includes a number of 
singular terms. 

{did) A collective term is one consisting of an aggregate of 
separable and single individuals considered as forming some 
sort of temporary unit. 

{dii) A collective term is one used to designate a group of 
objects which may be separated. 

{di2) A collective term expresses an aggregate of a number 
of similar objects, regarded as a temporary unit. 

(^/i3) A collective term is one which can be applied to a group 
of specified individuals taken as one. 

{di^) A collective term is one which is made up of a number 
of simil'ar terms. 

{ei) A DISTRIBUTIVE TERM is One which expresses univer- 
sality ; as, All men are mortal. All men is distributive. 

{e2) A distributive term is one which includes all the objects 
of the class specified. 

(^?3) A distributive term is one which we do not think of as 
being made up of a number of similar elements. 

(e'4) A distributive term is the name applied to a number of 
similar objects thought of as a whole. 

(^5) A distributive term is a name applied to a number of 
objects not thought of as separate, individual, similar tilings. 

{eG) A distributive term is a name applied to objects thought 
of as made up of a number of similar, separable, and indepen- 
dent elements. 

(^7) A distributive term indicates some of the objects of a 
class as such. 

(/i) An ABSTRACT TERM is one which expresses an indefinite 
relation or object, such as disobedience or power. 

(/2) Abstract has in it the idea of quality and attribute. 

(/3) Abstract terms are nouns which express some sort of 
relation. 

(/zj.) Abstract term is that which is not the name of matter 
but expresses an active relation. 

(/5) An abstract term is a noun which involves relations 
between things without expressing or naming them. 

(/6) Abstract signifies a quality, act, or state of a thing. 

(Z;) An abstract term is one Vv^hich cannot be thought of 
without its relation to something else being considered. 

(/8) An abstract term is one, used in a grammatical sentence, 



44^ EXERCISES. 

which does not necessitate the introduction of an object to 
which it is applied into the thought of the proposition. 

(/9) An abstract term is the name of a quality not involving 
the mentioning of the thing itself. 

(/lo) Abstract term is a term that can be used without the 
object being mentioned to which it applies. 

(^i) A CONCRETE TERM is an adjective, verb, adverb, or 
preposition completing the meaning of a verb. 

(^2) Concrete terms are names of things, verbs, adjectives, 
and other parts of speech. 

(^3) Concrete term is the names of nouns, adjectives, and 
verbs. 

{/ii) A RELATIVE TERM is One that expresses a relation, as 
father and son. 

(/12) A term may be relative in three ways, ist, the relation 
between itself and an invariable standard; 2d, the comparison 
with a certain variable standard. 

(7/3) A relative term is one whose relation with another term 
is so close as to always involve the apprehension of that term 
as a part of a larger whole. 

(/14) Relative term is one that expresses one party of a rela- 
tion usually active. 

(7^5) Relative term is one which denotes relationship. 

{/i6) If the standard changes when the same term is applied 
to different things, that term is relative. 

(/ly) Terms are relative when they express comparison with a 
variable standard, and also a relation between two objects 
which are mutually dependent in meaning. 

(728) Relative terms show a dependence upon, or connection 
with, some other term or object. 

(/i) An ABSOLUTE TERM is One which expresses quality be- 
longing absolutely to that object. 

(72) An absolute term is one which does not express any 
relation. 

(73) If the standard remain the same when the same term is 
applied to different things, the term is absolute, /.^., perfect. 

(74) An absolute term states a relation between things re- 
ferred to a standard which does not vary. 

(75) An absolute term is one stating the relations of the 
object in itself. 

(/i) The CONNOTATION of a word is the special meaning 



EXERCISES. 443 

which it conveys to the mind of each person in addition to the 
common definition. 

{J2) Connotation is the significance of a term as distin- 
guislied from others. 

(73) The connotation of a term are the attributes belonging 
to it. 

(74) Connotation is the summing up of all the attributes of 
the term to be defined. 

(75) Connotation is the consideration of attributes. 

(76) The connotation of a name is expressed by the attributes 
by virtue of which the name is applied. 

(77) The connotation of a class is the name applied to the 
common attributes of the members of the class, by virtue of 
which attributes the members belong to the class. 

(78) Connotation is the relation of the common attributes to 
the general term. 

(79) The connotation of a name is the concept of the object 
designated by that name. 

(710) Connotation is the enumeration of attributes which an 
object must have in order to be known by the general name. 

(711) The connotation of a term is the attribute or attributes 
which are applied to the object about which you are speaking. 

3. Give the exact equivalent of the following in concrete 
terms : 

{a) Charity never faileth. 

(b) Life is real, life is earnest. 

{c) Whether we realize it or not, our lives always have a 
moral purpose. 

(^) But flesh with the life thereof, which is the blood thereof, 
shall ye not eat. (Gen. ix. 4.) 

{e) He stretcheth out the north over empty space, and 
hangeth the earth upon nothing. (Job xxvi. 7.) 

(/) Our demand is for justice to silver ! 

{g) By the passes which he made he drew the pain from the 
patient's forehead out into his own hands. 

(Ji) The energy released by this process soon travelled from 
A to B and put it in motion, or rather, put motion into it. 

(/) Labor is oppressed by the money powxr. 

4. Rewrite these paragraphs, so as to preserve the sense but 
get rid of as many of the abstract terms as you can. In the 
case of the last two be careful to interpret the words as the 



444 EXERCISES. 

author meant them to be interpreted, not as they are usually- 
interpreted nowadays. 

(a) '' What . . . recommends the geometrical method to 
Spinoza is, not only its apparent exactness and the necessity 
of its sequence, but, so to speak, its disinterestedness." (Ed. 
Caird.) 

(^) " Men generally confound this distinction, and regard all 
their settled opinions or beliefs as knowledge. This is not 
merely false, but absurd. . . . And this is apparent also from 
the nature and generation of our opinions. For, in general, 
these come to us not from any conscious process, but naturally 
and spontaneously from many sources, as, e.^., from testimony, 
from authority, from inaccurate observation or careless reason- 
ing, and even largely from mere prejudice or bias. Hence, 
familiar to us as our opinions are, their origin in general is as 
unknown to us as were anciently the sources of the Nile ; nor 
have we any just notion of the grounds on which they rest, or 
of the nature and justice of their demands on our belief. Hence, 
until some means of verifying our opinions be found and ap- 
plied, we can have no assurance of their rectitude. The first 
step in science or philosophy must, therefore, be to distinguish 
between verified and unverified opinions. The former consti- 
tutes true knowledge or science ; the latter — though it is in 
fact the stuff out of which most of the current philosophy is 
woven — has no just pretension to the name." (G. H. Smith's 
"Logic*'.) 

(c) '* Notwithstanding, certain it is that if those schoolmen, 
to their great thirst of truth and unwearied travail of wit, had 
joined variety and universality of reading and contemplation, 
they had proved excellent lights, to the great advancement of 
all learning and knowledge ; but as they are, they are great 
undertakers indeed, and fierce with dark keeping: but as in the 
inquiry of the divine truth, their pride inclined to leave the 
oracle of God's word, and to vanish in the mixture of their own 
inventions ; so in the inquisition of nature, they ever left the 
oracle of God's works, and adored the deceiving and deformed 
images, which the unequal mirror of their own minds, or a 
few received authors or principles, did represent unto them. ' 
Bacon, ** Advancement of Learning", Bk. L 

{d) '* There fall out to be these three distempers, as I may 
term them, of learning : the first, fantastical learning ; the 



EXERCISES. 445 

second, contentious learning; and the last, delicate learning; 
vain imaginations, vain altercations, and vain affectations ; 
and with the last I will begin. Martin Luther, conducted no 
doubt by a higher Providence, but in discourse of reason find- 
ing what a province he had undertaken against the Bishop of 
Rome and the degenerate traditions of the church, and finding 
his own solitude being no ways aided by the opinions of his 
own time, was enforced to awake all antiquity, and to call 
former times to his succors, to make a party against the present 
time. So that the ancient authors, both in divinity and in 
humanity, which had long time slept in libraries, began gener- 
ally to be read and revolved. This by consequence did draw on 
a necessity of a more exquisite travail in the languages original, 
wherein those authors did write, for the better understanding 
of those authors, and the better advantage of pressing and 
applying their words. And thereof grew again a delight in 
their manner of style and phrase, and an admiration of that kind 
of writing, which was much furthered and precipitated by the 
enmity and opposition that the propounders of those primitive 
but seeming new opinions had against the schoolmen ; who 
were generally of the contrary part, and whose writings were 
altogether in a differing style and form ; taking liberty to coin 
and frame new terms of art to express their own sense, and to 
avoid circuit of speech, without regard to the pureness, pleas- 
antness, and, as I may call it, lawfulness of the phrase or word." 
Bacon, loc. cit. 

5. *This cheap quack thought he could gull the public, so he 
put some dirty water in a bottle and then turned all his low 
cunning to the invention of a lying advertisement in which he 
claims that one bottle of his nasty stufi will cure a man of 
everything under the sun except his credulity.' When a person 
makes such a statement as this, what probably are the ascer- 
tained facts in the case ? 

6. Pick out the demonstrative and the descriptive words and 
phrases in the following : 

(a) And this is my little daughter ! But she is my big daugh- 
ter now. 

(d) The swift-footed Achilles is lame. 

{c) Smith and Jones, manufacturers of Mrs. Kelly's home- 
made pickles. 

{d) Many oriental antiques are now manufactured in Chicago, 



446 EXERCISES. 

7. What fallacy, if any, is to be found in the following? 

{a) Books are a source both of instruction and amusement ; 
a table of logarithms is a book ; therefore it is a source both of 
instruction and amusement. (J.) 

(d) Three and two are two numbers ; five is three and two ; 
therefore five is two numbers. (Ray.) 

(c) I hate the English and I always shall ; for was it not they 
who fought against us in the Revolutionary War and again in 
1812.^ 

(a) Unless his cold works out through the throat or nose, 
how can he hope to get rid of it ? 

(^) Do not let him learn all those useless facts ; they will over- 
load his mind. 

(/) You say that A is taller than B and shorter than C ; but 
that is absurd, for the same person cannot be both taller and 
shorter at the same time. 

(£-) It is all very well for you to talk in prayer-meeting about 
your badness, but when any one tells you outside that you are 
bad you resent it. 

(/i) The people of the country are suffering from famine ; and 
as you are one of the people of the country you must be suffer- 
ing from famine. (J.) 

(/) * You gave him all the information be had ! ' Then you 
were very foolish ; for you had none too much for yourself. 

(J) All the trees in the park make a thick shade ; this poplar 
is one of them, and therefore it makes a thick shade. (J., 
altd.) 

(/e) It is true that in a democracy the people vote, but it is 
absurd to say that they rule ; for you and I are people and 
everything we vote for is defeated. 

(/j In a republic a majority of the people rules. That is what 
we mean by the word. Therefore it is a contradiction to say 
that the majority of the people did not rule in the South African 
Republic. 

(;;/) ' You said that these cakes were hot, and when I bought 
them I found that they were frozen.' ' I never said they 
were hot ; I simply called : Hot cakes ! — that is the name of 
them.' 

(;/) The civilization of this people, like every other organism, 
was developed gradually from small beginnings and some day 
it is bound to decav. 



EXERCISES. 447 

(o) The ancient Greeks produced the c:rcatest masterpieces of 
eloquence and philosophy; the Lacedaemonians were ancient 
Greeks ; therefore they produced the greatest masterpieces of 
eloquence and philosopliy. (J.) 

(p) We shared his money and then we shared his sorrows ; 
so that if we did not leave him very much of the former we did 
not leave him much of the latter either. 

(^) He who believes himself to be always in the right in his 
opinion, lays claim to infallibility; you always believe yourself 
to be in the right in your opinion ; therefore you lay claim to 
infallibility. (W.) 

(r) The life is gone, and, since there are no vacant places 
in Nature, something has come to take its place, namely, 
death. 

(s) No soldiers should be brought into the field w^ho are not 
well qualified to perform their part; none but veterans are 
well qualified to perform their part ; therefore none but vet- 
erans should be brought into the field. (W.) 

(/) The accumulated experiences which we inherit from our 
ancestors have always shown that the wages of sin is death. 

(u) You say that you did not understand that this move was 
contemplated ; and yet it was recommended by the directors, 
and you are one of them. 

(v) ' Love my neighbor ! ' Yes. But that is no reason why 
I should not get ahead of one of these soulless corporations if I 
can. 

(w) How can I be religious when religion has done so much 
harm in the world ? What makes the Mohammedans so intol- 
erant ? What makes the people of India so helpless ? What 
made the great wars of history ? What keeps Ireland and Eng- 
land always at strife ? What made the Inquisition ? What 
has opposed every fundamentally new scientific conception for 
centuries ? Always religion ! 

(x) '* No reason, however, can be given why the general hap- 
piness is desirable, except that each person, so far as he believes 
it to be attainable, desires his own happiness. This, however, 
being a fact, we have not only all the proof which the case ad- 
mits of, but all which it is possible to require, that happiness is 
a good, that each person's happiness is a good to that person, 
and the general happiness, therefore, a good to the aggregate 
of all persons," (Mill's " Utilitarianism.") 



448 EXERCISES. 

(j) ** Little Indian, Sioux or Crow, 

Little frosty Eskimo, 
Little Turk or Japanee, 
O ! don't you wish that you were me? 

You must often, as you trod, 
Have wearied not to be abroad. 
You have curious things to eat, 
I am fed on proper meat. 
You must dwell beyond the foam. 
But I am safe and live at home." 

(R. L. Stevenson.) 



CHAPTER VI. 

I. Take O. W. Holmes' " Last Leaf" or some other piece of 
poetry or prose and show the relations expressed by each word 
or phrase, thus : 

I saw him once hefore 
As he passed by the door, 

And again 
The pavement stones resound, 
As he totters o'er the ground 

With his cane. 

* I ' — individual identity. 

* Saw ' — noetic relation ; also time ; also perhaps a suggestion 
of causation, since I could not have seen him unless he had 
acted in some way upon me. 

* As he passed by the door ' — time ; also causation if the 
phrase implies that his passing the door was what made me see 
him. 'Passed by the door' — motion; i e., change of place, 
involving the relations of both time and place. 

'The door' — individual identity, if the term is really intended 
to mean the movable thing that we use to close an aperture. 
In this case the word also suggests the complex relation of 
means and end if we stop to think about it. But in this con- 
text the term is more probably used to mean the open doorway. 
If this be so the relation expressed is mainly one of position 
in space, though the term and context also suggest the absence 



EXERCISES. 449 

of a causal relation, — he came into a certain position where 
nothing prevented me from seeing him. 

2. Criticise the following definitions : 

(^i) A REAL PROPOSITION tclls the name of the object. It 
does not tell what state the object is in. 

{a2) A real proposition asserts something of a term. 

(^3) A real proposition is one in which there is identity, also 
description. 

(^4) Real terms relate to things. 

(ac,) A real proposition is one which states a relation. 

{a6) Real propositions state some additional fact about an 
object. 

(^i) A VERBAL PROPOSITION is One which defines an object. 

(32) A verbal proposition is one which explains the meaning 
of nouns or the terms of the proposition. 

(^3) A verbal proposition is one which defines an object, 

(^4) A verbal proposition is the meaning of a name. 

(^5) Verbal propositions define the object itself. 

(36) A verbal proposition is one which explains a part or the 
whole of some thing. 

(dy) A verbal proposition explains the meaning of a word 
v\^ithin the proposition. 

(3S) Verbal terms relate to words. 

(3g) A verbal proposition explains the term or some part 
of it. 

3. Consider how far each of the five fundamental relations 
given in the text is independent of the others. Is it possible, 
for example, for anything to have individual identity without 
also being the subject of states, and vzce versa ; can we know a 
thing unless it acts ; can a thing be said to haye a state or qual- 
ity unless some one knows it } etc. 



CHAPTER VIII. 

I. What is the subject, what is the copula, and what is the 
predicate of each of the following propositions ; * what is its 
quality and quantity ; and if the predicate has any quantity 
what is it } If the proposition is ambiguous or peculiar in any 

* Taken for the most part from the collection in Jevons's '' Studies in 
Deductive Logic ", p. 38. (Macmillan, 1884.) 



450 EXERCISES. 

other way, point out the fact ; and if the termc are abstract make 
them concrete. 

(a) All Athenians are Greeks. 

(d) They never pardon who have done the wrong. 

(c) Great is Diana of the Ephesians. 

(d) No abracadabras are gasteropods. 

(e) All, all are gone, the old familiar faces. 
(/) He that is not for us is against us. 

(g-) Men mostly hate those whom they have injured. 
(A) Old age always involves decrepitude. 
(z) Nothing morally wrong is politically right. 
(J) It is not good for man to be alone. 
(^) A certain man had two sons. 

(/) There's something rotten in the state of Denmark. 
{7n) All cannot receive this saying. 
(n) Few men are free from vanity. 

(o) He that fights and runs away may live to fight another 
day. 

(/) There is none good but one. 

(g^) Two straight lines cannot enclose a space. 

{r) Familiarity breeds contempt. 

(s) Only the ignorant affect to despise knowledge. 

(/) All is not gold that glitters. 

{u) Love is not love which alters when it alteration finds. 

(v) A friend should bear a friend's infirmities. 

2. * Few books are at once learned and amusing.' This is 
treated in the passage quoted from Jevons on p. 98 as proposi- 
tion O. Consider whether it might be regarded as equivalent 
to both O and I, or to an exclusive or exceptive proposition. 

3. Give hypothetical and disjunctive equivalents for all the 
universal propositions in the first exercise on this chapter. 

4. Are the following propositions disjunctive or hypothetical ? 
Give their categorial equivalents ; also their exclusive and ex- 
ceptive equivalents. 

{a) If you are a man you are mortal. 

(3) Either you are a man or you are mortal. 

(c) Either you are a mian or you are not mortal. 

(d) If you are not mortal you are a man. 

(e) You will not go to heaven unless you are good, 
(/) You will not go to hell if you are not bad. 

5. When I say ' No men are infallible ' how many men am I 



EXERCISES. 45 1 

talking about? When I say * All men are not infallible ' how 
many am I talking about ? 

6. Examine, and if necessary correct, the statement on p. 102 
that 'Almost any Turk hates a Greek' is universal with refer- 
ence to the Greeks. 

7. Criticise the following definitions : 

(ai) Singular proposition denotes an individual as such. 

{a2) A singular proposition is one which specifies a single 
one of several relations. 

[a],) A singular proposition is one in which singular terms 
are used. 

(a4.) A singular proposition is one which deals with or treats 
of a singular term. 

(^5) A singular proposition is one which makes a statement 
about some one of a class of objects not especially designated. 

{a6) A singular proposition is applicable to certain designated 
members of a class as such. 

(ay) A singular proposition is one that states something 
about certain designated members of a class. 

(aS) A singular proposition is one that makes a statement 
about an individual object. 

(ag) Singular proposition is one in which we find certain 
specified objects pointed out. 

(aio) Singular proposition is one which states something 
about an individual and leaves no doubt as to whether it is 
referring or is meant to refer to a thing or is applicable or 
meant to apply to a thing. 

(ail) A singular proposition is one which refers to certain 
specified individuals and leaves no doubt as to who is under 
discussion. 

(^i) Universal proposition is one in which the predicate 
is affirmed of the whole subject. 

(32) A universal proposition is one which distributes its sub- 
ject but not its predicate. 

(^3) Universal propositions are those which involve state- 
ments about all the objects included in the subject term. 

(^4) Propositions are universal w^hen they make statements 
about all the objects mentioned in the subject term. 

(^5) A universal proposition is a statement which affirms or 
denies something about all the objects in the class to which the 
subject term belongs. 



452 EXERCISES. 

(b6) A universal proposition is one in wliich a statement is 
made of some particular object definitely specified. 

(^7) Universal as applied to a proposition is the quality of 
embracing all of the objects belonging to the class specified in 
the subject of the proposition. 

{dS) A universal proposition is one in which an affirmation is 
made concerning every object of the kind denoted by the sub- 
ject term. 

(dg) A proposition is universal when the statement made is 
true of every object indicated by the subject term. 

(<^io) Universal as applied to propositions refers to all the 
objects indicated by the subject term. 

(^i) A PARTICULAR PROPOSITION is One which has for its 
subject a singular term. 

(c2) A particular proposition is one whose predicate does not 
apply to all of the subject. 

(<f3) A particular proposition is one in which the predicate is 
stated of part of the subject. 

{c4.) A particular proposition is one in which the predicate is 
not affirmed or denied of all the subject. 

(^5) A particular proposition is one which makes an assertion 
about an indefinite part of a subject. 

{r6) A particular proposition is one in which the predicate 
affirms or denies only a part of an indefinitely designated group 
of objects. 

{c7) A particular proposition is one in which a statement is 
made concerning a part of an indefinite number of objects. 

(cS) A particular proposition is one that asserts something of 
an indefinite number of objects. 

(eg) A particular proposition is one in which the predicate 
makes a statement about any part of the thing talked about. 

(cio) A particular proposition is one which does not make a 
statement about all of a class of objects, but about some par- 
ticular member of a class. 

(^11 ) A particular proposition is a proposition which has a 
subject which does not include a whole class, but only some. 

(<ri2) A particular proposition is one in which a statement is 
made regarding some portion of the class of objects designated 
by the subject of the proposition. 

(di) The QUANTITY of a proposition refers to the fact whether 
it is negative or affirmative. 



EXERCISES. 453 

(d2) Quantity is the character of a proposition which states 
whether it is singular, universal, or particular. 

(//3) The quantity of a proposition is its form as to whether it 
afhrms something about the whole of a subject or something 
about undesignated members ; in other words, whether it is uni- 
versal, particular, or singular. 

(d^) Quantity is the affirmation or denial of a thing as uni- 
versal or particular. 

(^^5) Quantity is that character of a proposition as distin- 
guishing the universal from the particular. 

{d6) The quantity of a proposition is that property of a prop- 
osition by which a proposition is 'considered as universal, re- 
ferring to all of a class, singular, referring to some specified 
part of a class, or particular, referring to some unspecified part 
of a class. 

(dy) Quantity has reference to the kind of propositions, 
whether they be universal or singular, as distinguished from 
other kinds. 

(dS) Quantity is that characteristic of a proposition which 
marks it as universal, particular, singular, or indefinite. 

(dg) Quantity is the character of a proposition which states 
something about all the members of a class, undesignated mem- 
ber or members, or a specified individual or member. 

(ei) An affirmative proposition is one in which the pred- 
icate affirms or asserts something about the subject. 

(ei) An affirmative proposition is one where a certain rela- 
tion is said to exist between the subject and predicate. 

(^3) An affirmative proposition is one which expresses a cer- 
tain agreement between the subject and predicate so that the 
qualities of the predicate belong to the subject. 

(^4) An affirmative proposition is one w^hich tells some fact 
about the object named in the subject. 

(^5) An affirmative proposition is a statement of a fact and 
whose predicate refers to the name of the subject. 

(^6) An affirmative proposition is one which makes a positive 
assertion. 

(ey) An affirmative proposition is one which asserts the predi- 
cate as having qualities belonging to the object which the sub- 
ject represents. 

(eS) An affirmative proposition is one which affirms a certain 
relation or condition between two terms. 



454 EXERCISES. 

{eg) An affirmative proposition is one in which the predicate 
is asserted to belong to either the whole subject or a part of the 
subject. 

(^lo) An affirmative proposition is one in which the qualities 
of the predicate are asserted as belonging to the subject. 

(/i) Quality has to do with whether a proposition is sin- 
gular, particular, or universal. 

(fi) Propositions are said to differ in quality when they are 
affirmative or negative. 

(/3) Propositions differ in quality when one affirms and the 
other denies a statement. 

(/4) The quality of a proposition indicates whether it is 
affirmative or negative. 

(/5) The quality of a proposition is in regard to its nature as 
affirmative or negative. 

(/6) The quality of a proposition is the relation between 
A E I O. 

(/7) The quality of a proposition is the attribute or attributes 
of the subject term taken together. 

{/8) The quality of a proposition is the character of a propo- 
sition as it affirms or denies. 

i/g) Quality as applied to propositions is that attribute of 
the proposition which determines whether the proposition is 
affirmative or negative. 

(/lo) The quality of a proposition is its character as to the 
affirmation or negation of the statement made in the proposition. 

(/ii) Quality of a proposition is its form as to whether it is 
affirmative or negative. 

(£■1) An exceptive proposition affirms or denies some- 
thing of an object mentioned. 

(^2) In an exceptive proposition something is affirmed or 
denied of the object excluded. 

(^3) An exceptive proposition refers to some unspecified 
objects. 

(^4) An exceptive proposition is one in which something is 
affirmed or denied of some part of the subject specified. 

(^5) Exceptive propositions are those which affirm the predi- 
cate of all the subject except certain well-defined cases to which 
the subject does not belong. 

(£-6) An exceptive proposition is one that states something 
about all specified members of a class except certain ones. 



EXERCISES. 455 

[gj) An exceptive proposition is one that states something 
about all but the unspecified member or members of a class. 

{g^) Exceptive term as applied to propositions is used to 
mean that the predicate affirms the subject in all cases with one 
exception. 

{hi) An exclusive proposition affirms or denies some- 
thing of an object not mentioned. 

(7/2) An exclusive proposition is one in which something is 
told about the individuals specified in the subject term. 

(/23) An exclusive proposition is one which tells something 
about a designated part of the subject term. 

(7/4) An exclusive proposition is one which denies the truth 
or falsity of a part of the object spoken of. 

7/5) An exclusiv^e proposition states something about certain 
specified members of a class. 

{h6) An exclusive proposition is one which states something 
only about a specified member of a class. 

{hj) An exclusive proposition uses the words *' only ", *' none 
but " in asserting the predicate of the subject. 

(>^8) An exclusive proposition is the statement of one of a 
class to the exclusion of all other members of that class. 

8. Criticise the following arguments : 

{a) Ever}^ lover of truth is an admirer of Huxley; every 
bishop in the established church is not ; therefore the bishops 
of the established church are not lovers of truth. 

{5) Those who have sacrificed their health and fortune for a 
principle deserve the gratitude of mankind ; few men have 
done this ; therefore few men deserve the gratitude of mankind. 

{c) All poets are not imaginative ; some philosophers are 
poets; therefore some philosophers are not imaginative. (Ray.) 

{d) The Cretans are liars ; A, B, C are Cretans ; therefore 
A, B, C are liars. (Hamilton.) 

{e) All that glitters is not gold ; tinsel glitters ; therefore it is 
not gold. (W.) 

(/) Warm countries alone produce wines ; Spain is a warm 
country ; therefore Spain produces wines. (W.) 

{g) Revenge, Robbery, Adultery, Infanticide, etc., have been 
countenanced by public opinion in several countries; all the 
crimes we know of are Revenge, Robbery, Adultry, Infanticide, 
etc. ; therefore all the crimes we know of have been coun- 
tenanced by public opinion in several countries. (W.) 



45 6 EXERCISES. 

(yh) The learned are pedants ; A is a learned man ; therefore 
A is a pedant. (Ray, quoted. ) 

(/) Testimony is a kind of evidence which is very likely to 
be false ; the evidence on which most men believe that there 
are pyramids in Egypt is testimony ; therefore the evidence on 
which most men believe that there are pyramids in Egypt is 
very likely to be false. (W.) 

(7) All the miracles of Jesus would fill more books than the 
world could contain ; the things related by the Evangelists are 
the miracles of Jesus ; therefore the things related by the 
Evangelists would fill more books than the world could con- 
tain. (W.) 

{k) No trifling business will enrich those engaged in it ; a 
mining speculation is no trifling business ; therefore a mining 
speculation will enrich those engaged in it. (W.) 

(/) Every Turk hates a Greek ; Dr. Constantinides is a Greek ; 
therefore every Turk hates Dr. Constantinides. 

{m) The English and Germans are quarrelling; I am English 
and you are German ; therefore you and I are quarrelling. 

CHAPTER IX. 

\a. Assume the truth of each in turn of the propositions 
A, E, I, O, Singular Affirmative and Singular Negative, and 
inquire what follows in each case about the truth or falsity of 
the others. 

\b. Assume the falsity of each in turn of these propositions 
and inquire what follows about the truth or falsity of the others. 

2. If you wish to put an opponent in the wrong, w^hat kind of 
statements should you try to get him to make, and what kind 
of statements should you yourself try to avoid making ? 

3<3;. * None but the strong survive.' Resolve this into two 
ordinary propositions. 

lb. Make a list of all the propositions with which it is incon- 
sistent, and from these pick out its contradictory. 

4. Find the contradictory or contradictories of the following : 
* If a person is a good citizen, he will not smuggle ', ' Heavy 
objects do not necessarily fall when they are thrown into the 
air.' 

5. Estimate the truth of the following statements and correct 
them if they are wrong. 



EXERCISES. 457 

(a) If one proposition is true, then any other proposition from 
which it follows is true also, and if tlie proposition in question 
is false, then the other from which it follows is false also. 

(/?) If one state of affairs exists, then any other state of affairs 
which its existence involves exists also, and if the first state of 
affairs does not exist, neither does tlje other. 

(c) If the truth of A involves the truth of B, and the falsity 
of B involves the falsity of A, then the falsity of A must also 
involve the falsity of B, and the truth of B the truth of A. 

6. What in each case is the smallest amount of information 
necessary to disprove the followini^.^ — 

{a) Great men are always large of stature. 

(d) Lazy people are never useful. 

(c) A certain celebrated statesman died in a lunatic asylum. 

(d) Some dogs are afraid of ghosts. 

7. Criticise the following definitions : 

(ai) Opposition of propositions occurs when one is false 
and the other true. 

{a2) Opposition of propositions is the name applied to the 
process by which, taking a given proposition as true, we deter- 
mine the truth, falsity, or doubtfulness of the other propositions. 

(/;i) The term 'contradictory' as applied to propositions 
means that in one proposition a statement cannot be both 
affirmed or denied in regard to a certain object. 

(di) A contradictory proposition is one in which the absence 
of something is affirmed or denied whose presence was denied 
or affirmed in the original proposition. 

(^3) Contradictory propositions are those which differ either 
in quantity or in quality or in both. 

(^4) Term contradictory as applied to propositions. A nega- 
tive particular proposition is the contradictory of a positive 
general. 

(^5) A contradictory proposition is one which affirms or 
denies the falsity or truth of the proposition with which it is 
compared. 

(d6) Contradictory propositions are those which differ in both 
quantity and quality. 

{dy) Two propositions are contradictory when they make 
statements opposite in meaning. 

(^8) Contradictory propositions are two propositions which 
cannot both be true at the same time. 



45 S EXERCISES. 

(bg) A contradictory proposition is one in which one state- 
ment is true and the other false. 

(^lo) Statements are said to be contradictory when one 
affirms and the other denies in any way a certain thing said 
about an object. ^ 

{bii) When we have one proposition which is universal 
affirmative and one which is particular negative, these two 
propositions are contradictory. Or if we have a universal neg- 
ative and a particular affirmative, they are contradictory. That 
is, when we have two propositions such that when one is true 
the other must be false, they are called contradictory. 

{ci) Contrary propositions are those which directly refute 
each other. If one is true, the other is false. 

{c2) Two propositions are contrary when one is in the uni- 
versal affirmative form and the other in particular negative 
form. 

(^3) Contrary propositions are those which assert the utmost 
variety of circumstances. 

(^4) Contrary propositions are those in which there is a con- 
trary relation expressed, as, * Wretched people are unfortunate ' 
is the contrary proposition of ' Happy people are fortunate'. 

{c^) Contrary propositions are those which deny a state of 
things asserted by a previous proposition. 

{c6) Contrary propositions are those in which what is 
affirmed of all the subject or some of the subject in one propo- 
sition is denied of all the subject or some of the subject in the 
other proposition. 

{cj) A universal negative and a universal affirmative are called 
contrary propositions ; one is false and one is true. 

(<r8) Contrary propositions are propositions which are di- 
rectly opposite in quality. 



CHAPTER X. 

I. Explain the following so as to make clear in each case 
what relation (cause, motive, premise, law) is indicated by the 
italicized words : 

(a) Why did you go to London ? (W.) 

{b) Why is this prisoner guilty } (W.) 

{c) Why does a stone fall to the earth } (W.) 



EXERCISES. 459 

(d) Why do the germs of diphtheria do so much harm ? 

{e) This ground is rich because the trees on it are flourishing. 
(W.) 

(/) The trees flourish because the ground is rich. (W.) 

(^•) '' He that is of God heareth God's words : ye therefore 
hear them not, because ye are not of God." John viii. 47. 

{Ji) *' Why do ye not understand my speech .^ Even because 
ye cannot hear my word." John viii. 43. 

(/) •' And because I tell you the truth, ye believe me not." 
John viii. 45. 

(y) ** And no man laid hands on him ; for his hour was not 
yet come." John viii. 20. 

{k) " And ye will not come to me that ye might have life." 
John V. 40. 

(/) *' How can ye believe, which receive honour one of an- 
other, and seek not the honour which cometh from God only } " 
John V. 44. 

{j)i) Two cerebral centres once connected tend to keep that 
connection, since we tend to have the same thoughts again that 
we have had before. 

2. Obvert the following : 

{a) This writer is inconsistent. 

{l)) The authors of these books are specialists. 

(<f) Good for this date only. 

{d) We have met the enemy and they are ours. 

{e) I was not alone. 

(/) This is not the worst filter in the market. 

{g) It was not a bad dinner. 

(//) It is not unreasonable to suppose that a man with all his 
experience and all his success would be abundantly able to 
perform so simple a task. 

(/) The luxuriousness of the trees is not the cause of the 
soil's fertility. 

(y) This man is my brother. 

{k) We climbed the mountain. 

3. Criticise the following definitions : 

{a) Obversion is the affirming or denying of a statement 
which has previously been denied or affirmed. 

{}>) An obverse proposition is one which denies or affirms 
what has been previously affirmed or denied and vice versa. 

{c) Obversion consists in affirming or denying the absence of 



46o EXERCISES. 

qualities whose presence has been affirmed or denied in the 
original proposition. 

{d) In obversion the same subject is kept, but that is 
affirmed or denied of the opposite of that which was denied or 
affirmed in the previous proposition. 

{e) Obversion is the moving of the sign of negation from the 
copula to the predicate or from the predicate to the copula. 

(/) Obversion is making a proposition include all it excluded 
before and vice versa, 

CHAPTER XL 

1. Apply the traditional conversion to all the propositions in 
the first exercise to Chapter VIII. 

2. Obvert each of the following, convert what you get, and 
keep on alternately obverting and converting until you cannot 
go any further. Do the same again, beginning with conversion. 

{a) All good children are happy. 

{b) No abracadabras are hypotheses. 

{c) " Who noble ends by noble means obtains 

Or, failing, smiles in exile or in chains, . . . 
That man is blest indeed." 
{d) He is not happy who is dead. 

3. If it is not true that John is no heavier than James, what 
can we say about James, things heavier than James, things not 
heavier than James, things heavier than John, things not heav- 
ier than John, and the relation 'heavier'.^ 

4. What is the relation of opposition, conversion, and obver- 
sion between each two of the following propositions ? — 

{a) All the trout are in this pond. 

{b) The fish in the other pond are not trout. 

{c) Some of the fish in this pond are not trout. 

5. Give {a) the converse of the obverse, and [b) the obverse of 
the converse of this proposition : Every pig has a cloven hoof. 
Then apply conversion by negation to the resulting proposi- 
tions. 

6. Criticise the following definitions : 

{a) Conversion is telling something in a new proposition 
about objects predicated in another proposition. 

(b) The conversion of a proposition is when the subject and 
predicate change places. 



EXERCISES. 461 

(c) The converse of a proposition is one in which the predi- 
cate is taken for the subject and the subject for the predicate. 

(d) Conversion is saying something in a new proposition 
about the objects that were or might have been indicated by 
the predicate of the original proposition. 

7. Criticise the following arguments : 

(a) None but the industrious deserve to succeed ; I am indus- 
trious ; therefore I deserve to succeed. 

(3) None but the industrious deserve to succeed ; I deserve 
to succeed ; therefore I am industrious. 

(c) The express train alone does not stop at this station ; 
and as the last train did not stop it must have been the express 
train. (J.) 

(d) When we hear that all the righteous people are happy, it 
is hard to avoid exclaiming, What ! are all the unhappy per- 
sons we see to be thought unrighteous ? (J.) 

(e) All equilateral triangles are equiangular, and consequently 
all equiangular triangles must be equilateral. (F.) 



CHAPTER XII. 

1. Estimate the correctness of the following statements : 

(a) No inference can be drawn unless two objects are com- 
pared with a third. 

(d) No inference can be drawn if any of the relations in ques- 
tion are heterogeneous. 

2. Criticise the following definitions : 

(a) Mediate inference is inference drawn from more than 
two statements. 

{3) Mediate inference is an inference which requires a middle 
term. 

(c) Mediate inference is inference from a set state of affairs — 
under specific conditions. 

(d) In mediate inference the mind has more than one act to 
perform. It arrives at the conclusion by means of other state- 
ments than just the one in regard to which the inference is 
made. Mediate inference is used chiefly in syllogisms. 

(<?) Mediate inference is reasoning from one premise to an- 
otlier by means of an intervening constructive process. 

(/) Mediate inference is that form of reasoning which re- 



462 EXERCISES. 

quires some intermediate statements before the conclusion may 
be drawn. These intermediate processes are called premises. 

{g) Mediate inference is the total of a series of conclusions 
considered according to specifications, part of which are con- 
sidered in the major premise and part in the minor. 

{k) Mediate inference is inference drawn from more than one 
premise. 

CHAPTERS XIII-XVI. 

I. Arrange the propositions in the following syllogisms so as 
to have the major premise first, the minor premise second, and 
the conclusion last ; tell the quantity and quality of each propo- 
sition ; tell also the figure of each syllogism, whether it is valid, 
and what caution it breaks if it is not. 

{a) All A's are B ; all B's are C ; therefore all A's are C. 

{b) No A is C ; for no A is B and all B's are C. 

{c) Some A's are B and some B's are C ; therefore some A's 
are C. 

{d) All A's are B and some B's are C ; therefore some A's 
are C. 

(e) No B is A ; all C's are B ; therefore some C is not A. 

(/) All B's are C ; all A's are C ; therefore all A's are B. 

{g) This cannot be S's boy Jack ; for I saw Jack ten minutes 
after he was born and his body was covered with dark hair, 
and this child's is not. 

(//) Every A is C and some B's are not C ; therefore some 
A's are not B. 

(/) It is not true that a man cannot do a great work without 
a strong physique , for the philosopher Kant did a great work 
and his physique was anything but strong. 

(/) B has the kindest of feelings towards everybody ; there- 
fore the man you saw in a violent altercation with his wife 
could not have been he. 

{k) There must be some invariable connection between red 
hair and a hasty temper, for every red-haired person I know is 
quick-tempered. 

(/) All B's are C ; no A is C ; therefore no A is B. 

{m) A and B each examined all the specimens he could find, 
and A noticed that in every case a certain feather in the tail 
was bent or broken, while B noticed that in nearly every case 



EXERCISES. 463 

there was a scar near one of the eyes. Whatever the cause, it 
is evident that these two strange pecuHarities often coincide. 

ia. What caution or cautions are embodied in the following 
proverbs : 

(i) All that glitters is not gold. 

(2) One swallow doesn't make a summer. 

2b. Find or make corresponding proverbs for as many of the 
other cautions as you can. 

3. A is B and B is C, therefore A is C. Reasoning on the 
same principle, may we not say : Polytheism is superstition, 
and superstition is everywhere, therefore polytheism is every- 
where } 

4. What fault, if any, is to be found with the following argu- 
ments } Show^ how they can be tested by Euler's diagrams. 

{a)' Some men are heroes ; J. S. is a man ; therefore J. S. is a 
hero. 

{b) All men are heroes; J. S. is not a man ; therefore J. S. is 
not a hero. 

((f) All men are heroes; J. S. is a hero; therefore J. S. is a 
man. 

{d') He must come from B. ; for every one that comes from 
there has that same way of pronouncing his r's. 

{e) Some men are wise, and some men are good ; therefore 
some wise men are good. 

(/) No man is perfect; this goat is no man ; therefore this 
goat is perfect. 

(^) No men are thoroughly unselfish ; some women are ; 
therefore some men at least are not women. 

(//) All men are animals and no animals are myths ; therefore 
no men are myths, and Homer really lived. 

(/) Few towns in the United Kingdom have more than 
300,000 inhabitants : and as all such tow^ns ought to be repre- 
sented by three members of Parliament, it is evident that few 
towns ought to have three representatives. (J.) 

(/) Only animals are sentient beings ; fishes are animals ; 
therefore fishes are sentient beings. (Ray.) 

5. Give all the conclusions that can be drawn from each of 
the following pairs of premises : 

{(i) Every A is B, and no B is C. 

{b) Every A is B, and this C is not A. 

{c) No A is B, and some C's are A, 



464 EXERCISES. 

(d) No A is B, but this C is B. 

{e) Every A is B, but some C's are not B. 
(/) Some B's are A and some B's are C. 
{g) Some B's are A, but no B's are C. 

6. Supply the missing premise in the following syllogisms : 
{a) All A's are C ; for all A's are B, and — 

{b) Some A's are not C ; for some A's are B, and — 
{c) None but non-A's are non-C's ; for all non-B's are 
non-A's, and — 

{d) All A's are non-C's ; for no A's are non-B's, and — 

(e) Some A's are not non-C's ; for no non-C is B, and — 

7. Show that the * rules of the syllogism ' given in the foot- 
note to page 177 can be inferred from the 'cautions ' given in 
preceding chapters. 

8. Make a set of arguments each one of which breaks a 
different caution, and show how each of them also breaks the 
* rules of the syllogism '. 

9. Is it possible for both major and minor terms to be par- 
ticular at the same time in the premises ? If so, construct an 
argument where this is the case. (C.) 

10. Reduce the following argument in the fourth figure to 
each in turn of the other three : 

Some B is A • 

No C is B; 

Therefore some A is not C. 



CHAPTER XVIL 

I. Criticise the following definitions : 

{ai) An ENTHYMEME is an imperfect syllogism. 

{a2) An enthymeme is an incomplete syllogism. 

(<^3) An enthymeme is a syllogism some one or two of whose 
premises or conclusion are imperfectly expressed. 

(^4) An enthymeme is a misstated syllogism ; that is, one in 
which one of the premises is wanting. 

(^i) A DILEMMA consists in assuming two assertions, but 
proves something in either case. 

{bi) A dilemma is a disjunctive proposition in which there 
are two alternatives, 



EXERCISES. 4^5 

(^3) A dilemma is when there is no escape from two proposi- 
tions. If one is false, the other must be true, and vice versa ; 
there can be no half-way ground. 

(<^4) A dilemma is a combination of the disjunctive and hy- 
pothetical, such that no true conclusion can be drawn. 

(ci) By SORITES is meant a syllogism composed of tlie three 
propositions O, I, E. 

{c2) Sorites contains a series of syllogisms imperfectly ex- 
pressed. 

(^3) Sorites is a compound syllogism and may be decom- 
posed into single syllogisms. 

(di) An EPICHEIREMA is a syllogism one of whose premises 
proves or gives a reason for another premise. 

(di) An epicheirema is a syllogistic statement so framed as 
to contain the conclusion of one part as the prosyllogism of 
another, and so on. 

(<:/3) Epicheirema is a syllogism furnishing reason for premise 
of another syllogism, or a syllogism one of whose premises is 
the conclusion of another. 

(^4) Epicheirema is the name given to the process of proving 
a statement by a prosyllogism. 

(^/5) An epicheirema is a statement which gives a reason for 
that statement. 

(d6) An epicheirema is a syllogism that depends upon an in- 
complete episyllogism. 

(dy) Epicheirema is a syllogism in w^hich the propositions are 
not all present. 

(dS) Epicheirema is a syllogism that gets its reason for a 
proposition from the syllogism before it. 

(^i) A DESTRUCTIVE DILEMMA is a disjunctive proposition 
in which either horn of the dilemma is not true. 

(<?2) A destructive dilemma is a syllogism in hypothetical 
form, only with two different antecedents in the major premise 
for the same consequent. It is called destructive because the 
consequent is denied. 

(^3) A destructive dilemma is the one known as the modus 
ponendo tollens, where by affirming the consequent is denied. 

(^4) A destructive dilemma is a syllogism in which the major 
term is a disjunctive proposition and the minor term is a cate- 
gorical proposition ; from which the conclusion is derived bv 
modus ponendo toUens. 



466 EXERCISES. 

(^5) A destructive dilemma consists of two syllogisms which 
break the validity of each other. 

(^6) A destructive dilemma is a complex dilemma and con- 
sists of two alternatives called horns, both of which are denied 
in the course of the argument. 

(^7) A destructive dilemma consists of a complex dilemma, 
that is, a syllogism in which the major premise consists of a 
hypothetical proposition with two or more antecedents, and a 
minor premise consisting of disjunctive proposition. 

2. Give two examples each of a constructive hypothetical 
syllogism, a destructive hypothetical syllogism, a disjunctive 
syllogism, a simple constructive dilemma, a complex construc- 
tive dilemma, a destructive dilemma, an epicheirema, an enthy- 
meme, and a sorites. Make sure that each of these is valid. 

3. ' If they do not work, they go hungry.' Assuming this to 
be true, what happens when one of the following statements is 
also true ? — 

(a) They do not work ; 

(d) They do not go hungry ; 

(c) They work ; 

(d) They go hungry. 

(4) Reduce the following arguments to a recognized form and 
determine whether they are valid or not: 

(a) All D's are E, all C's are D, all B's are C, and no A's are 
B ; therefore no E is A. 

(^) All J's are L, all C's are non-V, all J's are W, all L's are 
C ; and therefore some W's are not Vs. 

(c) Some E's are A ; for all non-E's are non-D, no C's are 
non-D, all B's are C, and all non-B's are non-A's. 

5. With each of the following tell the kind of argument. Is it 
valid ? If not, what caution is broken or what fallacy is com- 
mitted ? Reduce the argument to categorical form if it is ca- 
pable of such reduction ; and also if it is hypothetical reduce it 
to disjunctive form, and vice versa. Show what fallacy the ar- 
gument commits in these new forms. 

{a) If his conscience disapproved of the act, it was certainly 
wrong for him to do it, but his conscience did not disapprove, 
therefore it was not wrong for him to do it. 

(b) No honest man can advocate a change in the creed of his 
church ; for he must either believe it or not believe it, and if he 
believes it he cannot honestly help to change it, while if he 



EXERCISES. 467 

does not believe it he cannot honestly belong to the church 
at all. 

(c) Protection from punishment is plainly due to the inno- 
cent ; therefore, as you maintain that this person ought not to 
be punished, it appears that you are convinced of his innocence. 
(W.) 

(d) If men are not likely to be influenced in the performance 
of a known duty by taking an oath to perform it, the oaths com- 
monly administered are superfluous ; if they are likely to be so 
influenced, every one should be made to take an oath to behave 
rightly throughout his life. But one or other of these must 
be the case ; therefore either the oaths commonly administered 
are superfluous, or every man should be made to take an oath 
to behave rightly throughout his life. (W.) 

(e) The child of Themistocles governed his mother ; she gov- 
erned her husband ; he governed Athens ; Athens, Greece ; and 
Greece, the world : therefore the child of Themistocles gov- 
erned the world. (W.) 

(/) It is worth while to teach the elements of Latin in the 
public schools if this gives the minds of the pupils a good gen- 
eral training, or if it gives most of the pupils a useful insight 
into Roman life and literature, or if most of them will continue 
the study in a college course. But none of these alternatives 
is true ; therefore it is not worth while to teach the elements 
of Latin in the public schools. 

(o-) If every ghost story is to be believed, we must accept 
the general standpoint of the 'spiritualists'; but we cannot 
accept their general standpoint ; therefore we cannot believe 
ghost stories. 

(/z) If transportation is not felt as a severe punishment, it is 
in itself ill suited to the prevention of crime ; if it is so felt, 
much of its severity is wasted, from its taking place at too great 
a distance to affect the feelings, or even come to the knowledge, 
of most of those whom it is designed to deter; but one or 
other of these must be the case : therefore transportation is 
not calculated to answer the purpose of preventing crime. (W.) 

(/) If virtue is voluntary, vice is voluntary ; virtue is volun- 
tary ; therefore so is vice. (Aristotle.) 



4^8 EXERCISES. 



CHAPTER XVIII. 

Criticise the following definitions : 

{ai) A FALLACY is a statement which is not true. 

{a2) When wrong meaning is given to a statement it is called 
a fallacy. 

(^3) Fallacy is a mistake in term. 

(<^4) A fallacy is a false conclusion drawn from two premises. 

(^5) A fallacy is the incorrect use of the laws governing 
thought. 

{a6) A fallacy is an untruth — a flaw. If you detect a flaw in 
a proposition, you have found a fallacy in the proposition. 

(aj) If a method of reasoning is so used as to make state- 
ments or conclusions contradictory, a fallacy is made. 

(a8) A fallacy is a syllogism in which an incorrect conclusion 
is drawn. 

(^9) A fallacy is a false judgment. 

{bi) A MATERIAL FALLACY is a fallacy which arises from the 
use of more than three terms, more than three propositions, or 
ambiguous words, or an improperly stated syllogism. 

{b2) A material fallacy is a fallacy in the word or words of a 
proposition. 

(<^3) A material fallacy is one in which there is a breach in the 
subject-matter. 

CHAPTER XIX. 

1. Criticise the following definitions : 

{ai) Petitio principii is the fallacy of begging the question. 

{a2) The fallacy of petitio principii is using one of the prem- 
ises in the conclusion. 

(^2) Ignoratio elenchi is a fallacy of imperfect reasoning ; 
that is, what follows is not true. 

(^2) Ignoratio elenchi is a fallacy in which the premises and 
conclusion have no distinct connection. 

(^3) Ignoratio elenchi is the fallacy committed when a con- 
clusion is drawn which may have some bearing upon what has 
been said in the premises, but which does not logically follow. 

2. Consider whether the assumption of a false premise may 
be fairly regarded as a case of begging the question. 



EXERCISES. 4^9 

3. Make or find two examples besides those given in the text 
of each of the fallacies there explained. 

4. Criticise the following arguments or implied arguments : 
(a) Written examinations are not an absolutely fair test of a 

student's scholarship — much less of his industry and intelli- 
gence. It is therefore wrong to base his grade upon them. 

(3) Municipal ownership of street-cars would be beneficial to 
the people, and w^hat is beneficial to the people should be put 
into practice ; therefore the street-cars under private ownership 
should not be patronized. 

(c) It is wrong to take the life of a fellow man, for God has 
distinctly commanded us not to, and it is wicked to disobey 
his commandments. If any one pretends to doubt that this 
commandment really did come from God, I can only appeal to 
his own conscience and his own common sense. When God 
gave the commandments to his people is it likely that he 
would have omitted the most important of them all — a com- 
mandment Vvdiich only expresses the natural feeling of every 
normal human being .^ 

(d) " America has still a long vista of years stretching before 
her in which she will enjoy conditions far more auspicious than 
any European country can count upon. And that America 
marks the highest level, not only of material well-being, but of 
intelligence and happiness, which the race has yet attained, 
will be the judgment of those who look not at the favored few 
for whose benefit the world seems hitherto to have framed its 
institutions, but at the whole body of the people." (James 
Bryce.) 

(e) " It no doubt wounds the vanity of a philosopher who is 
just ready with a new solution of the universe to be told to 
mind his own business [laissez faire]. So he goes on to tell us 
that if we think that we shall, by being let alone, attain to per- 
fect happiness on earth, we are mistaken. The half-way men — 
the professorial socialists — join him. They solemnly shake 
their heads, and tell us that he is right — that letting us alone 
will never secure us perfect happiness." (W. G. Sumner.) 
What fallacy do they commit ? 

(f) 'Every particle of matter gravitates equally.' * Why ? ' 
* Because those bodies which contain more particles ever gravi- 
tate more strongly, z.e., are heavier.' * But', it may be urged, 
' those which are heaviest are not always more bulky '. * No, but 



470 EXERCISES. 

still they contain more particles, though more closely con- 
densed.' 'How do you know that?' 'Because they are 
heavier.' * How does that prove it .^ ' * Because, all particles of 
matter gravitating equally, that mass which is specifically the 
heavier must needs have the more of them in the same space.' 
(W.) 

ig) Those are your arguments against the course of conduct 
I propose ; and yet the fact remains that w4ien you were in my 
position you did the very thing that you are now advising me 
not to do, 

{/i) Everybody ought to contribute something to the support 
of the unfortunate ; therefore there is no harm in a law which 
compels him to do so. 

(/) *' Again, we are not inclined to ascribe much practical 
value to that analysis of the inductive method which Bacon 
has given in the second book of the Novum Organum. It is, 
indeed, an elaborate and correct analysis. But it is an analysis of 
that which we are all doing from morning to night, and which 
we continue to do even in our dreams." (Macaulay.) 

5. Examine the arguments or implied arguments in the follow- 
ing passages from Trumbull's " Lie never justifiable ". The 
first of them may be regarded as an introduction to the history 
of the discussion. 

{a) " Because of the obvious gain in lying in times of extrem- 
ity, and because of the manifest peril or cost of truth-telling in 
an emergency, attempts have been made, by interested or prej- 
udiced persons, all along the ages, to reconcile the general dut^ 
of adhering to an absolute standard of right, with the special 
inducements, or temptations, to depart from that standard for 
the time being." (p. 81.) 

{b) " All the refinements of casuistry have their value to those 
who admit that a lie may be right under certain conceivable 
circumstances ; but to those who, like Augustine and Aquinas> 
insist that a lie is a sin per se, and therefore never admissible, 
casuistry itself has no interest as a means of showing when a sin 
is not sinful." (p. 114.) 

{c) ** When he attempts the definition of a lie, however, 
Jeremy Taylor would seem to claim that injustice to others and 
an evil motive are of its very essence, and that, if these be 
lacking, a lie is not a lie." (p. 117.) 

{d) " As to falsifying to a sick or dying man, he [Dorner] 



EXERCISES. 471 

says 'we overestimate the value of human life, and, besides, in 
a measure usurp the place of Providence, when we believe we 
may save it by committing sin.' " (p. 132.) 

(e) ''A lie being a sin per se, no price paid for it . . . would 
make it other than a sin. ... It was a heathen maxim, * Do 
right though the heavens fall,' and Christian ethics ought not 
to have a lower standard than that of the best heathen morality." 
(pp. ^Z, 79.) 

(/) " God cannot justify or approve a lie. Hence it follows 
that he who deliberately lies in order to secure a gain to him- 
self, or to ore whom he loves, must by that very act leave the 
service of God, and put himself for the time being under the 
rule of the * father of lies '." (p. 79.) 

{g) "It is a physician's duty to conceal from a patient his 
sense of the grave dangers disclosed to his professional eye, and 
which he is endeavoring to meet successfully. And in well- 
nigh every case it is possible for him to give truthful answers 
that will conceal from the patient what he ought to conceal ; 
for the best physicians do not know the future, and his profes- 
sional guesses are not to be put forward as if they were assured 
certitudes." (p. 75.) 

CHAPTER XX. * 

1. Criticise the follow^ing definitions : 

{a) A fallacy of many questions is one in which many 
irrelevant questions are asked which cannot be answered di- 
rectly by Yes or No and which confuse the argument. 

[b) The fallacy of many questions is the use of more data 
than are needed to prove the premises. 

ic) A fallacy of many questions is the result of a false suppo- 
sition. 

(^/) The fallacy of many questions consists in asking two or 
more questions at the same time so that it is impossible to give 
a correct answer. 

{e) The fallacy of many questions is using so many questions 
in the argument that the conclusion does not stand out clearly. 

(/) The fallacy of many questions consists in asking two or 
more questions in one. 

2. What fallacies, if any, are committed or exposed in the 
following : 



472 EXERCISER. 

(a) * We were put in this world to help others.' * And what 
are others here for ? ' 

{d) '* If any one thinks that there are or ought to be in society 
guarantees that no man shall suffer hardship, let him under- 
stand that there can be no such guarantees, unless some other 
men give them." (W. G. Sumner, op. cit.) 

(c) Old age is wiser than youth. We should therefore pay 
great deference to the convictions of the ancients. 

(d) ' There never was an Irishman so poor that he did not 
have a still poorer Irishman living at his expense.' 

(e) ' Habit is the cable which has grown so strong by use 
that its victim cannot depart from it.' 

(/) Thought is nothing but a movement of the brain. 

(^) "There is a beautiful notion afloat in our literature and 
in the minds of our people that men are born to certain * natu- 
ral rights.' ... If there were such things as natural rights, the 
question would arise, Against whom are they good ? Who 
has the corresponding obligation to satisfy these rights.^ 
There can be no rights against Nature, except to get out of her 
whatever we can, which is only the fact of the struggle for 
existence stated ov^er again. The common assertion is that the 
rights are good against society ; that is, that society is bound 
to obtain and secure them for the persons mterested. Society, 
however, is only the persons interested plus some other persons ; 
and as the persons interested have by the hypothesis failed to 
win the rights, we come to this, that natural rights are the 
claims which certain persons have by prerogative against some 
other persons. Such is the actual interpertation in practice of 
natural rights — claims which some people have by prerogative 
on other people." (W. G. Sumner, op. cit.) 

(A) And if a spark has been kindled by the exercises of this 
day, let us water that spark. 

(/') Tlie sultan dreamed that all his teeth had fallen out, and 
summoned the soothsayers to tell him what it meant : 

** At last an old soothsayer, wrinkled and gray, 
Cried, 'Pardon, my lord, what I have to say ; 

'Tis an omen of sorrow sent from on high ; 
Thou sbalt see all thy kindred die.' 

Wroth was the sultan ; he gnashed his teeth, 
And his very words seemed to hiss and seethe, 



EXERCISES. 473 

And he ordered the wise man bound with chains, 
And gave him a hundred stripes for liis pains. 

The wise men shook as the sultan's eye 
Swept round to see who next would try ; 

But one of them, stepping before the throne, 
Exclaimed in a loud and joyous tone : 

* Exult, O head of a happy state ! 
Rejoice, O heir of a happy fate ! 

P'or this is the favor thou shalt win, 
O Sultan, to outlive all thy kin.' 

Pleased was the sultan and called a slave. 
And a hundred crowns to the wise man gave." 

{j) The claimant has undoubtedly many peculiarities of gait 
and manner which were characteristic of the missing baronet. 
Are not these therefore proofs of identity equivalent to the 
evidence of imposture afforded by the absence of tattoo-marks 
which the genuine man is proved to have possessed } (J.) 

{k) Human powers are bounded only by the infinite. (D. 
altd.) 

(/) Hoc unum scio, quod nihil scio, 

(;;/) God separated the different races of men ; then why 
should we encourage immigration that will mix them up again ? 

(n) " A lie is mconsistent with confidence ; and the knowl- 
edge that a lie is, under certain circumstances, deemed proper 
by a man, throws doubt on all that the man says or does under 
any circumstances. No matter why or where tlie one opening 
for an allowable lie be made in the reservoir of public coiifi- 
dence, if it be made at all, the final emptying of that reservoir 
is merely a question of time." (Trumbull, p. 227,) 

{o) According to Professor Sumner " the possession of capi- 
tal is an indispensable prerequisite of educational, scientific, 
and moral goods ". Now a man w^ho possesses no moral goods 
is not a good man, and a man without educational goods is not 
educated. From all of which it follows that according to Pro- 
fessor Sumner the capitalists are the only people in the com- 
munity who are either good or educated. 

(/) A man who has money enough to obtain the best food, 
the best tools, and the best care when he is sick has a great 



474 EXERCISES. 

advantage over his rivals in the struggle for existence. But 
what is to the advantage of one man in this struggle is to the 
disadvantage of his competitors; and thus it happens that by 
the very fact of bringing life to the rich man the money which 
he possesses often brings death to his poorer rival. 

{q) All the great fmancial crimes that we read about are 
committed by bankers and stock-brokers. Therefore ihe coun- 
try would be a great deal better off if banks and stock ex- 
changes were abolished. 

(r) * They tell us that we are weak, unable to cope with so 
formidable an adversary ; but when shall we be stronger } ' 
{s) "When 1 have grown to man's estate 

I shall be very proud and great, 
And tell the other girls and boys 
Not to meddle with 7?iy toys." 

(R. L. Stevenson.) 
(/) Whatever is universally believed must be true ; the exist- 
ence of God is not universally believed ; therefore it is not 
true. (W.) 

CHAPTERS XXI— XXV. 

1. "A, B, C, D, and E are the only German students I know; 
they are all men of considerable intellectual attainments, and 
consequently I may infer that all German students are men of 
considerable intellectual attainments." (F.) Is this argument 
inductive or deductive } Is it valid ? If so, how much confi- 
dence can be attached to the conclusion 7 

2. Why are we able to reach many conclusions by induction 
that cannot be reached by deduction } 

3. * I have no confidence in a Chinaman, for the Chinese gov- 
ernment is one of the most corrupt in the world.' Estimate 
the value of such an inference. 

4. Should we seek for the causes of things, or merely of their 
states and relations ? Is there any objection to speaking of 
a thing as * cause of itself ' 7 (See definition in Spinoza's 
^'Ethic^".) 

5. What fallacy is committed by a man who passes counter- 
feit money on the ground that the public has given it to him 
and the public ought to get it back again } 

6. Is there any objection to the following explanation } — 



EXERCISES. 475 

* People get tired because everything they do involves some 
action on the part of the cells in their brain. These cells, like 
all other cells, are probably living creatures, and as such they 
are subject to the universal law of fatigue.' 

7. '* The analysis of a fact consists in the process of distin-. 
guishing 7ne7itaUy between its different details (the various 
episodes of an event, the characteristics of an institution), with 
the object of paying special attention to each detail in turn ; 
that is what is called examining the different * aspects ' of a 
fact, — another metaphor/' (Langlois-Seignobos.) In the light 
of this, consider the possibility of modifying statements in 
Chapter XXII in which the word ' aspect ' is used. 

8. Give some examples of explaining in a circle — * circulus in 
explicando.' 

9. Give some examples of a ' Perfect Induction ' and of an 
Inductio per Enumerationem Simplicem. 

10 Give some examples of your own to show how we assume 
relations of identity and general laws in discovering relations of 
causation, and similarly with each of the other two. 

11. How would you prove that the rotation of the earth is 
not due in large measure to the constant influence of the fixed 
stars } How would you prove, on the other hand, that the 
rotation is not due to the influence of some demon inhabiting it ? 

12. Give examples of your own showing how causal analy- 
sis gives definiteness of conception and greater reliability of 
inference. 



CHAPTERS XXVI— XXXI. 

1. With the following combinations of antecedents and 
consequents, find the cause of K. What is the method } — 
ACDEKLMN, ACEKMN. 

2. What causal relation is suggested by the following com- 
binations ? Is it suggested only, or proved to exist .^ What 
is the method.^— ABCFNOPQ, CDEGLMNT, CHIJNRS, 
BCENOT. 

3. Find a set of causal relations that will account for the fol- 
lowing combinations. What is the method? — ABCDNOPO, 
BCDOPQ, EFRS, ABENR, AFDPQS, BEGRTU. 

4. Do the same with this: ABCDUNQ, ABEFUNOPR, 
CDEFQTOPR, BEGNOS. 



476 



EXERCISES. 



5. Do the same with this : ABCDZ, ACEPQRX, BCEQXZ, 
ACFPRVX, DEFQV, ADFPV. 

6. Do the same with this: ABCFQST, ACDPSTO, 
CDESTOV, BDEPQOV, ADEPSOV, ACEPSTV. 

7. Do the same with this: ABCPST, ABDPQS, ABEPS, 
ABFOPRS, ACEST, ACFORST, ADEQS, ADFOQRS, 
BCDPQT, BCEPRT, BCFOPRT, BDEPQR, BDFPQRO, 
CDEQRT, CDFQT, CEFORT, DEFOQR. 

8. Do the same with this : ABCPR, ABDO, ABEP, 
ACDOPZ, ACEPZ, ADEOPZ, BCDOPRX, BCEPRX, 
BDEOPX, CDEOP, ABCDOPR, ABCEPR, ABDEOP, 
ACDEOPZ, BCDEOPRX. 

9. What inference can be drawn from the following diagram? 

The distance of any dot above the 
line OB represents the proficiency 
of some one student in one kind of 
work, A; the distance from the line 
OA represents the proficiency of 
the same student in another kind 
of work, B. 

10. What inference could have 
been drawn from the diagram if the 
dots had been found to group them- 
selves about a diagonal running 
from A to B ? If they had been 
line ? If they had been scattered 



A 







B 



grouped about a horizontal 
irregularly over the whole square ? 

11. What is the significance of the italicized words in the 
following sentences ? — When he came I left ; He arrived and 
then there was trouble ; The x'^iw follozued X\\^ lightning. 

12. Examine the reasoning expressed in the following : 

(a) " Depend upon it, the best antiseptic for decay is an 
active interest in human affairs : those live longest who live 
most." 

(b) When this pond was first fished in the fish were very 
numerous and very easily caught ; but now so many of them 
have been caught that the rest have grown very wary. 

{c) Children are a good deal like apples — the first to ripen are 
usually the first to decay ; and therefore a wise teacher will do 
what he can to delay the development of those that seem most 
precocious, 



EXERCISES. 477 

{d) We all drank the water and none of us got sick ; so this 
outcry about the danger of typhoid is all nonsense. 

{e) Any one who examines the records will soon find out for 
himself that those students who * scatter ' most in their choice 
of studies are those who accomplish least in any of them ; and 
when he sees this he ought to realize the harm that can be 
done by a system of absolutely free electives. 

(/) Trains run with Blank's oil have made the fastest time 
known amongst railway men. 

{g) " A letter forged ! Saint Jude to speed ! 

Did ever knight so foul a deed ! . . . 
Thanks to Saint Bothan, son of mine, 
Save Gawain, ne'er could pen a line." (Scott.) 

{h) 'The rain-maker is going to fire off his gunpowder to- 
morrow, but he can't fool us ; we have a written contract that 
if there is no rain there is to be no pay.' Examine the same 
kind of reasoning with reference to patent medicines and *tips ' 
on investments : * no cure no pay ' — ' no profits no pay.* 

13. Give two examples of your own of each of the inductive 
methods explained in these chapters. 

14. Give some examples of ' combined ' and of * compounded * 
causes. 

15. With A as engineer and M as fireman a certain locomo- 
tive can average sixty-eight miles an hour ; with A as engineer 
and N as fireman it averages sixty-three miles ; with B as en- 
gineer and M as fireman it averages sixty ; and with B as 
engineer and N as fireman it averages fifty-five. What part of 
the speed in each case would you credit to the locomotive, and 
what to each of the men ? 

16. The weight of boys and girls of different ages in the 
public schools of the United States is about as follows : Boys 
of six, 43-|- lbs. ; of seven, 47^; of eight, 52J-; of nine, ^y^\ of 
ten, 62^ ; of eleven, 68^ ; of twelve, 73^ ; of thirteen, 80 ; of 
fourteen, 88 ; of fifteen, 100; of sixteen, 114. Girls of six, 42; 
of seven, 46 ; of eight, 50^; of nine, 55 ; of ten, 6o-J- ; of eleven, 
654 ; of twelve, 73 ; of thirteen, 83^ ; of fourteen, 94; of fifteen, 
103; of sixteen, no; of seventeen, 115^. From these data it 
is usually inferred that girls have a period of rapid growth 
between the ages of twelve and fourteen or fifteen, and that 



478 EXERCISES. 

boys have a similar period a couple of years later. Is there any 
other way of accounting for the figures ? 

17. "More men than women die every year. This is due to 
the greater mortality attending the life of the male " (Mayo- 
Smith, " Statistics and Sociology "). What does this mean ? 
How can it be possible.^ ' In Germany 109 men die each year 
for every 100 women.' What can we conclude from this ? 
Why is it better to know that in Germany 28.6 out of every 
thousand males die each year and 25.3 out of every thousand 
females? Since everybody must die sooner or later how is it 
possible that there should be in any country (or in the whole 
world) a permanently greater death-rate for one sex than for 
the other ? 

CHAPTERS XXXI— XXXII. 

1. In many gymnasiums a prize is given for 'symmetrical de- 
velopment '. How should this be estimated ? Is there any 
objection to giving the prize to the candidate whose propor- 
tions approach nearest to the average of all students measured ? 

2. In a study of great men it is found that for thirty-nine 
fathers and twenty- five mothers the average age of the parents 
at the time of the birth of the great man is 37.78 years for the 
former and 29.8 years for the latter. *' Although there are few 
cases, the results are interesting, because they are in agreement 
with those of Galton, who finds the average age of the parents 
of one hundred English men of science to be thirty-six years for 
the fathers and thirty years for the mothers. . . . Both studies 
would seem to show that the child born of parents in the prime 
of physical life has the better chance of greatness. Both results 
conflict with Lombroso's theory, which he took from Mosso, 
that * the number of men of genius and even of talent issued 
from aged fathers is very great.' " (A. H. Yoder in Ped. 
Sem. Ill, 137.) Can any fault be found with thCvSe conclusions ? 

3. A got a certain story from B, B from C, C from D, and D 
from E. In each case there was an even chance that the hearer 
' got it wrong '. What are the chances that A got E's story 
exactly as he told it ? 

4. Is there any difference between saying that a certain horse 
is the most likely to win the race and saying that it is likely to 
win ? 



EXERCISES. 479 

5. '* What an author expresses is not always what he believed, 
for he may have lied ; what he believed is not necessarily what 
happened, for he may have been mistaken. These propositions 
are obvious. And yet a first and natural impulse leads us to 
accept as true every statement contained in a document, which 
is equivalent to assuming that no author ever lied or was de- 
ceived." (Langlois-Seignobos.) Is there any objection to this 
statement ? 

6. Account for the saying that lightning never strikes twice 
in the same place. 

7. Is there any objection to this reasoning.^ — ' The event in 
question must have been either A, B, C, or D. Of these A is 
the most probable. Therefore the event in question was prob- 
ably A.' 

8. Scarlet fever is one of the most contagious of diseases, 
and yet an eminent authority says he 'can find no instance 
recorded where it has been transmitted through two healthy 
persons*. If we assume that such cases do not exist, what can 
we infer about the number of germs usually present in the 
vicinity of a patient and about the number necessary to trans- 
mit the disease ? 

9. What reply can be made to the following ? — ' You say that 
the prisoner is probably guilty. I grant it. But this only 
means that the prisoners in most cases of this sort are guilty. 
It does not mean that this particular prisoner has even a touch 
of guilt. Your very use of the word ' probable ' is a confession 
that for all you know he may be absolutely innocent. How 
then can you ask the jury to condemn him to an awful fate ? ' 

10. What reply can be made to the spiritualist who demands 
assent to his explanation of certain phenomena on the ground 
that it is the most probable of all the many explanations which 
have been offered ? Can we deny his conclusion without 
denying the premises ? 

11. Assuming that the difference between several different 
measurements of the same quantity is due to a large number of 
different variables, each one of which affects each of the meas- 
urements to a slight degree, prove that the mean of all the 
measurements is far more likely to be nearly correct than either 
of the extremes. 



4So EXERCISES. 



CHAPTERS XXXIII— XXXVI. 

1. How much inference is there in the following * observa- 
tions * ? — 

(a) A player catching a baseball at the far side of the field ; 
(d) The observer himself shooting a bird ; 

(c) The effect of a certain speech upon the hearer. 

2. Give some instances in which you yourself have ' ob- 
served ' or * remembered ' an event that did not take place. 

3. Can you recall any cases in which you have made records 
for your own use and then been unable to find them or to inter- 
pret them ? If so, what was wrong .^ 

4. Recall any cases you may know about in which circum- 
stantial evidence seemed convincing, though the conclusion to 
which it pointed was afterwards found to be wrong. 

5. '' Violenta presumptio is many times plena probatio ; as if 
one be run thorow the bodie with a sword in a house, whereof 
he instantly dieth, and a man is seen to come out of that house 
with a bloody sword, and no other man was at that time in the 
house." (Lord Coke.) Explain exactly what this means, and 
then see how many alternative explanations you can find for 
the occurrence mentioned in illustration. 

6. Estimate the value of the following arguments : 

(a) There must be something in oracles ; for Herodotus tells 
many tales that show the wonderful powers of the oracle at 
Delphi, and Herodotus was a careful and critical historian. 

(d) It is fair to assume that he was guilty of at least some 
misconduct, for where there is smoke there is fire, and he has 
certainly succeeded in getting himself criticised by everybody. 

(c) The doctrine of the divine right of kings was certainly 
current in the time of Elizabeth ; for we read in Shakspere : 
*' Not all the water in the rough rude sea 

Can wash the balm off from an anointed king." 

((/) '< To thine own self be true, 

And it must follow, as the night the day, 
Thou canst not then be false to any man." 

These are the words of Shakspere, perhaps the greatest ob- 
server of human life that ever existed ; and we should value 
them accordingly. 



EXERCISES. 481 

{e) You say it was not Homer who wrote about the travels 
of Odysseus. What of it } Somebody must have known about 
them, and what difference does it make whether we call him 
Homer or call him something else } 

(/) We must not expect too much happiness in this world, 
for the Bible warns us that ** man is born unto trouble, as the 
sparks fly upward." 

7. What is the significance of the statement that the Iliad 
and Odyssey were not written by Homer, but by another man 
of the same name ? What would be the significance of a simi- 
lar statement about Moses and the Pentateuch ? 

8. From the "Life of Professor Huxley", the ** Letters of 
J. R. Green ", and any other sources of information that you can 
command, find out exactly what it was that Huxley said in his 
retort upon the Bishop already mentioned on page 1 1. 

9. Estimate the following arguments : 

(a) If you believe in the survival of the fittest, you must 
believe that this old manuscript was one of the best of its time, 
for it is the only one that has survived. 

(d) This book is authentic; then why should we not believe 
what it says ? 

(c) This text of Cicero dates from the twelfth century and 
that only dates from the fourteenth, then why isn't this a bet- 
ter one to go by than that ? 

(d) This text has great value for the historian, for it was 
restored at infinite pains, and there is now every reason to 
believe that it is substantiality correct. 

(<?) ' Come and have your fortune told by Blank's system of 
palmistry. No man of science has ever disputed the claims of 
this system.' 

10. Herodotus telh of certain sailors who circumnavigated 
Africa and said on their return that as they went westward 
around the southern extremity of the land the sun was on their 
right. Herodotus said he did not believe this. What can 
we infer about Herodotus, and what can we infer about the 
alleged voya-ge ? 

11. During a thunder-storm the cook in a certain house 
rushed from the kitchen exclaiming that she had seen a ball of 
fire enter one window and go out of the other. What probably 
were the facts ? 

12. Two students who have never been suspected of dis- 



4^2 EXERCISES. 

honesty sit near each other at an examination and each of them 
writes these very words : *' Henry George was the great orator 
of the Revolution; it was he who said in Faneuil Hall, 'Give 
me liberty or give me life.' " What inference can be drawn 
from this coincidence ? How much should the inference be 
affected by the protests of the students that they were perfectly 
honest, or by their explanation that they had studied together ? 

13. Estimate the value of the following arguments : 

{a) Vacillating and cruel as our treatment of the Indians has 
often been, there can be no doubt that the European conquest 
of America has been a good thing for the world. Certain it 
is that we have not a single eminent writer of history who 
doubts it. 

(d) We must choose between A's account of this affair and 
B's. A's has never been seriously disputed ; B's has been dis- 
puted for centuries. How then can we hesitate between them ? 

(c) I know that I might have made up my mind to act other- 
wise ; for I was conscious at the time that there was nothing in 
me to prevent it. 

(d) The great influence of the mind over the body is well 
illustrated by such facts as the following : People often dream 
that they are falling from some great height, and if the dream 
stops there it does them no harm ; but if any one dreams that 
he strikes the ground, the mental shock is too great, and it 
kills him. 

14. Pick out and summarize the bare, concrete, observable 
facts (real or imaginary) stated in the following paragraphs ; 
point out any passages in which matters of fact and matters of 
opinion are confused ; assuming the concrete facts to be as 
stated, show what they prove ; show what must be assumed in 
order that the conclusion drawn should follow from the con- 
crete facts ; and estimate the reasonableness of such assump- 
tion or assumptions. 

* A careful observer of the people of India says : More sys- 
tematic, more determined liars than the people of the East 
cannot, in my opinion, be found in the world. Yet, strange to 
say, some of their works and sayings represent a falsehood as 
almost the unpardonable sin. Take the following example : 
''The sin of killing a Brahman is as great as that of killing a 
hundred cows ; and the sin of killing a hundred cows is as 
great as that of killing a woman ; and the sin of killing a hun- 



EXERCISES. 483 

dred women is as great as that of killing a child in the womb; 
and the sin of killing a hundred [children] in the womb is as 
great as that of telling a lie." ' 

* The duty of veracity is often more prominent among primi- 
tive peoples than among the more civilized. Among those 
Hill Tribes of India which have been most secluded, and which 
have retained the largest measure of primitive life and customs, 
fidelity to truth in speech and act is still the standard, and a 
lie is abhorrent to the normal instincts of the race. The 
Bheels, a race of unmitigated savages, are yet imbued with a 
sense of truth and honor strangely at contrast with their ex- 
ternal character. The Sowrahs do not know how to tell a lie. 
The Arabs are more truthful in their primitive state than when 
they are influenced by " civilization ". The word of a Hottentot 
is sacred.* 

* It is found, in fact, that in all ages, the world over, primitive 
man's highest ideal conception of deity has been that of a God 
who could not tolerate a lie ; and his loftiest standard of 
human action has included the readiness to refuse to tell a lie 
under any inducement, or in any peril, whether it be to a 
friend or to an enemy. This is the teaching of ethnic concep- 
tions on the subject. The lie would seem to be a product of 
civilization, and an outgrowth of the spirit of trade and barter, 
rather than a natural impulse of primitive man.' 

* It would seem to be clear that the best moral sense of man- 
kind everywhere deems a lie incompatible with the idea of a 
holy God, and consistent only with the spirit of man's arch- 
enemy — the embodiment of all evil.' (Condensed from Trum- 
bull : '* A Lie Never Justifiable.") 

15. "You say that development drives out the Creator; but 
you assert that God made you : and yet you know that you 
yourself were originally a little piece of matter, no bigger than 
the end of this gold pencil-case." (Huxley.) What kind of 
argument is this ? Estimate its force. 

16. ** Nevertheless, I did not formerly consider sufficiently 
the existence of structures which, as far as we can at present 
judge, are neither beneficial nor injurious ; and this I believe 
to be one of the greatest oversights as yet detected in my work. 
I may be permitted to say, as some excuse, that I had two dis- 
tinct objects in view : firstly, to show that species had not been 
separately created, and, secondly, that natural selection had 



484 EXERCISES. 

been the chief agent of change, though largely aided by the 
inherited effects of habit, and slightly by the direct action of 
the surrounding conditions. I was not, however, able to annul 
the influence of my former belief, then almost universal, that 
each species had been purposely created ; and this led to my 
tacit assumption that every detail of structure, excepting 
rudiments, was of some special, though unrecognized, service." 
(Darwin's ** Descent of Man ", part i. chap. 2.) What tendency 
does this illustrate ? 

17. ''The assertion of a fact wholly beyond the reach of 
evidence, for or against, is to be held as untrue." (Bain's 
** Logic ", p. 382.) Discuss this. 



INDEX. 



Abstract nouns, 60 ; definition of, 

67. 

Abstractions, hypostatising, 66. 
Abstractly denominated principle, 

fallacy of, 369. 
Absurd questions, 208. 
Absurdity as test of truth, 414. 
Accent, fallacy of, 39, 43. 
Accident, fallacy of, 42, 43. 
Accidents, definition of, 50. 
Accuracy, misplaced, 306. 
Agreement, double method of, 277; 

method of, 261 ff. 
Ambiguities, 13 ff. ; of quality and 

quantity, 98. 
Amphibology, 39, 42 n. 
Analogy, argument from, 413 ; 

false, 209. 
Analysis, causal, 257; hexateuchal, 

379. , 
Analytic propositions, 82. 
Antecedent, 106, 270 ; denying 

the, 185. 
Appeal to consequences, 10. 
Apperception, 412 n. 
Apprehension, simple, 5 n. 
Aquinas, Thos., 107. 
Archimedes, 326. 
Areolus, Petrus, 417 n. 
' Argument ', legal, 400 n. 
Arguments, abbreviated, 188. 
Argumentum ad hominem, 12, 201, 

202 ; ad populum, 12, 201, 202; 

ad rem, 12; ad verecundiam, 367. 
Aristotle, 40n., 83 n., 133 n., 176, 

214, 420. 
Arnold, Matthew, 42. 
Authority, argument from, 367. 
Authorship, joint, 378. 
Averages, general, 312. 



Bacon, Francis, 23, 249, 262 n. ; 

Roger, 262 n. 
Bailey, 68 n. 
Bain, 68 n. 

Berkeley, 15 n., 68 n., 368 n. 
Bismarck, 199. 
Boole, 107. 
Bosanquet, 61. 
Bowditch, 320 n. 
Bradley, 107. 
* Bulls', 210. 
Burnham, W. H., 350 n., 351 n., 

354n. 

Canning, 200. 

Causal analysis, 257. 

Causal interaction, 245. 

Causation, 235 ; peculiarities of, 
247. 

Cause, 238; false, fallacy of, 272. 

Causes, combined, 283 ff. ; com- 
plex, 281; compounded, 283 ff. ; 
counteracting, 281; plurality of, 
267, 282; quantitative treatment 
of, 287; vicariousness of, 267. 

Categories, 77, 83. 

Characteristic imperfection, 268. 

Chance, 332 n. 

Change, 84. 

Circulus in probando, 198. 

Circumstances, 233 ff. 

Classification, 50, 162. 

Composition, fallacy of, 39 n., 64, 
211. 

Comstock, 329. 

Conceivability as test of truth, 405, 
406, 421. _ 

Conclusion defined, 121. 

Concomitant variations, method of, 
290, 296. 

485 



486 



INDEX. 



Confirmation of statements, 393. 
Connotation, 60 n. 
Consequences, appeal to. 10. 
Consequent, 106, 270 ; affirming 

the, 185. 
Consistency, 124, 392, 405, 421. 
Contradiction, law of, 126 ; of 

statements, 393. 
Contrary propositions, 73. 
Conversion, 131; by negation, 138; 

per accidens, 136. 
Copula, 128 n., 143. 
Correlative terms, 74. 
Coulanges, Fustel de, i6n. 
Credulity, 345. 
Cross-division, 47. 
Cross-references, 49. 

Davis, 201 n. 

Deduction, 122 ; limitations of, 

145, 221. 
Definition, 30, 241 ; and division, 

45 ; how to find, 30 ; how to 

frame, 31; illustration in, 32; of 

things, 34. 
De Morgan, 72. 
Demurrer, 400 n. 
Denotation, 61. 
Descartes, 243, 420, 423. 
Difference, indirect method of, 278; 

methods of, 261, 262, 288. 
Differentiae, 32, 50. 
Dilemmas, 186. 
Distributed term, 135. 
Division, and classification, 45 ; by 

dichotomy, 46 ; fallacy of, 64; 

relation to definition, 45. 
Donation of Constantine, 377. 

Elimination, method of, 254. 

Enthymeme, 188. 

Epicheirema, 188, 189. 

Episyllogism, 189. 

Epithets, question-begging, 63. 

Error, measures of, 327. 

Euler's diagrams, 120 n., 140 ff., 
177. 

Everett, C. C, 130 n. 

Evidence, circumstantial, 361 ; ex- 
pert, 367 ff. ; issue before, 402. 
Exaggeration, 38. 
Excluded middle, law of, 128. 



Exhaustion, methcs^^^ /)f, 250, 265.' 
Existence, denials of, 89. 
' Expectation of life', 326. 
Experiment, 272 ff. 
Explicative propositions, 82. 
Extension, 61. 

Fact and feeling, 10. 

Faith, 425. 

Fallacies, classification of, 191; 
jingle, 194; of forgotten issue, 
195 ff. ; of ill-conceived universe, 
195; < purely logical', 193; re- 
flex, 194. 

Feeling and judgments, 11. 

Forgotten issue, fallacy of, 195 ff. 

Forgotten man, the, 216. 

Fowler, I97n., 223 n., 277. 

Fundamenta divisionis, 48, 53. 

Galen, 176. 
Galton, 316. 
Genung, 210. 
Genus, 32, 49. 
Geometry, 248, 406. 
Grand Remonstrance, 36. 
Greenleaf, 44 n., 385 n. 
Group comparisons, 296. 
Guessing in induction, 252. 

Hamilton, Sir Wm., 107, 136. 

Hay, John, 350. 

Hearsay, 384. 

Hegel, 19, 368. 

Herschel, 261. 

History, 356; limits of, 358 ; mon- 
uments in, 359. 

Hodge, A. A., 25 n. 

Hodge, C. F., 370. 

Hodgkin, Thos., 377 n. 

Honesty, intellectual, 10. 

Hume, 4,5, i5n., 83n., 262n., 
331 n. 

Huxley, 10, 239. 

' Hypotheses non fingo ', 419. 

Hyslop, 75. 

Ideas 4; classification of, 52. 
Identity, individual, 78, 162, 254 ; 

and similarity, 81; peculiarities 

of, 245; law of, 125. 
Ignoratio elenchi, 198. 



INDEX. 



487 



Illicit major, 15811., 170, 17411. 

Illicit minor, 15811., 17011., 174 n. 

Illusion, 91. 

Inductio per enumerationem sim- 
plicem, 251, 257. 

Induction, 122; Aristotelian, 250 ; 
certainty of, 226; distinguished 
from deduction, 221 ; perfect, 
227, 250. 

Inference, 121 ; by added deter- 
minants, 75 ; by privitive con- 
ception, 130; data for, 270; im- 
mediate, 131 ; in observation, 
343; mediate, 145; real, 152. 

Infima species, 50. 

Infinitation, 130. 

Innate principles, 230. 

Intension, 61. 

Interaction, 235; causal, 245. 

Interest, errors due to, 302. 

Interpretation, blunders of, 13. 

Irrelevance, 198. 

Jevons, 4, 5n., 16, 42 n., 50 n., 
64n., 7on., 75, 103 n., 107, 
107 n., 137, 186, 214, 251 n., 
320 n., 324 n., 325, 329. 

Johnson, Sam., 31, 

Judgment, 2. 

Kant, 15 n., 83 n., 107, 368, 422. 
Keynes, 83 n., 87, 87 n., 88, 107, 

109 n., Ii5n., Ii6n. 
Kidd, Benjamin, 370. 
Kipling, R., 93. 
Knowledge, 4, 425. 

Law, notion of, 237, 244. 
Langlois-Seignobos, 15 n., 3711., 

68, 69. 
Leibnitz, 206, 417. 
Lies, honest, 352. 
Locke, 4, 15 n,, 40 n., 61, 62, 206, 

398. 
Logic, definition of, 6 ; scope of, 6. 
Lotze, 68 n., 84 n., 106 n., 215. 
Lyell, 411. 

Mal-observation, 348. 
Manning, Cardinal, 370. 
Mansel, 107. 
Many questions, fallacy of, 207. 



Martensen, 25 n. 
Martineau, Jas., 66 n., 68 n. 
Mean, arithmetical, 313 ; general, 
312; geometrical, 313; kinds, 

of, 313- 

Means and end, 84. 

Median, 316. 

Memory, 343. 

Mercier, 208. 

Merriman, 329. 

Method, indirect, of difference, 278; 
joint, 275; of agreement, 264; 
of concomitant variations, 290, 
296; of difference, 261, 288; of 
elimination, 254; of exhaustion, 
250 ; of residues, 288 ; of statis- 
tics, 296. 

Methods, the four, 262. 

Mill, J. S., 35, 83 n., 107, 261, 
262, 263, 278, 284, 287, 290 n., 
292, 295 n. 

Minto, 20 n., 48 n., 64 n., 83 n., 
100 ff., 104 n., 186 n., 210 n., 
251 n., 262 n., 349 n., 369, 370. 

Modus ponens, 183. 

Modus tollens, 183. 

Motet, 353. 

Naming, use of, 55. 

Neglected articulation, 212 ; as- 
pect, 211; member, 215; whole, 
219. 

Newton, L, 244, 419 

Nicolay, Col., 350. 

Noetic relation, 82. 

Non -observation, 348. 

Non-sequitur, I95. 

Nouns, common, 60. 

Number, 85. 

Object of thought, 3. 
Objections, fallacy of, 220. 
Observation, 343 ; unprejudiced, 

347.. 
Obversion, 130. 
Occam's razor, 417. 
Opposite terms, 73. 

Parsimony, law of, 418. 
Permutation, 130. 
Personal equation, 300 
Petitio principii, 196. 



488 



INDEX. 



Phrases, conventional, 36 ; uses 
of, 56. 

Plato, 133 n. 

Pleadings, 400. 

Post hoc, ergo propter hoc, 272 

Powell, Baden, 223 n. 

Precision, where needed, 34. 

Preconception, errors of, 302. 

Predicate, quantification of, 136. 

Premise, 121 ; major, 150, 169; 
minor, 150. 

Probability, 330 ff. ; as a test of 
truth, 392; value of finding, 334. 

Probable error, 328. 

Proof, limits of, 423. 

Proper nouns, 60. 

Prophecy, 356. 

Propositions, 2, 82 ; accidental, 82 
affirmative, 96; ampliative, 82 
analytic, 82 ; categorical, 106 
contradictory, 113, 114, 117 
contrary, 113, 114, 117; copu- 
lative, 106 n. ; disjunctive, 106 ; 
essential, 82 ; exceptive, 103, 
115; exclusive, 103, 115; expli- 
cative, 82 ; formal characteris- 
tics of, 96 ; hypothetical, 106; 
indefinite, 99 ; indesignate, 99; 
modal, 85, 86 ; negative, 96, 
106 n.; opposition of, iii; par- 
ticular, 96, 1 10 n. ; preindesig- 
nate, 99 ; pure, 85 ; real, 82; 
remotive, 106 n. ; singular, 96, 
113 n. ; subaltern, 114; subal- 
ternate, 114 ; subcontrary, 114; 
synthetic, 82; universal, 96, 109; 
verbal, 82. 

Propria, 50. 

Prosy Uogism, 189. 

Quality, 96; undesignated, 99. 
Quantity, 96, 97; double, 102; un- 
designated, 99. 

Reality, conception of, 91. 
Reasoning, correct, 6; to the point, 

12. 
Reduction of oblique figures, 178. 
References, fallacy of, 369. 
Relations, combined, 84; denials 

of, 89 ; five fundamental, 77; 

how interwoven, 253. 



Residues, method of, 288. 

Schopenhauer, 76. 

Science, and religion, 425; work 
of, 244. 

Selection, accidental, 304. 

Sigwart, 79, 84. 

Simplicity as test of truth, 405, 
416, 421. 

Socrates, 241. 

Sorites, 188, 189. 

Space, ideas of, 5 ; relation of, 80. 

Species, 49. 

Spencer, H., 15 n., 31, 89, 90. 

Statements, interpretation of, 36. 

Statistics, method of, 296. 

Stephen, L., 11. 

Subject, and attribute, 78; of re- 
lation, 87; of sentence, 3, 87; 
of thought, 3. 

Sui generis, 50. 

Summum genus, 50. 

Sumner, W. G., 21 n., 65 n., 215 n., 
216. 

Syllogism, 145 ; figures of, 148; 
disjunctive, 186; first figure of, 
150; fourth figure of, 176; hypo- 
thetical, 183; rules of, 177 n.; 
second figure of, 162 ; third 
figure of, 171. 

Synthetic propositions, 82. 

Tenterden, Lord, 43. 

Terms, 56; absolute, 73; abstract, 
65, 70; collective, 63; concrete, 
65; connotative and non-conno- 
tative, 60; contradictory, 73; 
contrary, 73 ; contrapositive, 73 ; 
correlative, 74 ; demonstrative, 
58, 69 n.; descriptive, 69 n.; 
distributed, 135; distributive, 63 ; 
general, 61; negative, 71 ; oppo- 
site, 73; paronymous, 28; posi- 
tive, 71, 75; relative, 73, 74; 
singular, 61. 

Testimony, 363. 

Thinking, clear, 2, 6 ; clear by 
analysis, 259 ; hazy, 240; logi- 
cal, 6 ; objective, 6; two kinds 
of, I. 

Thing, 233-4; permanence of, 
242. 



INDEX. 



489 



Thorndike, Ashley, 378; Edward, 
L., 24911. 

Thought, blunders in, 191; laws 
of, 7, 121, 124; object of, 3; sub- 
ject of, 3; and things, 9. 

Time, ideas of, 5 ; relation of, 80. 

Trumbull, 25 n. 

Truth, double, 9 ; impersonal, 7; 
tests of, 405 ff. 

Truthfulness, tests of, 386 ff. 

Truths, general, 254. 

Undistributed middle, 158 n., 
166 n., 175 n. 

Uniformity of Nature, 228, 232; as 
test of truth, 405, 406, 421; in 
the mass, 409; precision in, 238; 
proof of, 243. 

Universe, assumed, 204; ill-con- 
ceived, 195, 204 ; of discourse, 72. 



Universes, confusion of, 208. 

Variation, average, 327. 

Venn, J., 53 n., 55, 108, 312, 329, 

332, 340 n. 
Vera causa, 420. 

Wallace, A. R., 341, 341 n. 

Whately, R., 16, 39 n., 64n., 107, 
197, 198, 199, 211, 212 n., 2i3n., 
219, 220, 369. 

Whewell, 261. 

Whole and part, 84. 

Words, ambiguous, 16, 22; blun- 
ders in, 191; categorematic, 58; 
meanings of, 13; oblique senses, 
37 ff.; single, uses of, 56; syn- 
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Vol. I. Finance and Taxation, Money and Bimetallism, Eco- 
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Vol. II. Statistics, National Growth, Social Economics. 

The author had hoped to bring these papers together him- 
self. 

The Dial : " Professor Dewey has performed a real service 
to the public, as well as to the memory of his late chief. . . . 
In the present collection the editor has not included every- 
thing General Walker ever wrote, but has aimed, so far as 
possible, to avoid repetitions of thought. . . there are some 
discussions of the national finances in the period following the 
Civil War, which have a timely as well as historical interest 
at the present time. . . . To improve the census was General 
Walker's work for many years, and his experience cannot fail 
to be of interest to the present generation. . . . Economics in 
the hands of this master was no dismal science, because of his 
broad sympathies, his healthy conservative optimism, his be- 
lief in the efficacy of effort ; and, in a more superficial sense, 
because of his saving sense of humor and his happy way of 
putting things, ... he was the fortunate possessor of a very 
pleasing literary style, . . . clear and interesting to the general 
reader, as well as instructive to the careful student.** 

The Outlook : " This book makes accessible for students the 
miscellaneous work of one of America's greatest political 
economists. . . . Dr. Dewey has performed his critical work 
with the reverence of a disciple, and reprinted in full all the 
more important contributions." 

Political Science Quarterly : ** The collection embraces between 
fifty and sixty articles, all of them characterized by the force- 
ful reasoning and balanced judgment of the gifted author. 'V 

U C \1 P V 1-4 Pi I T kr CC\ 29 W. 23(i St., NEW YORK 
nblNKl nULl (X L.U. 373 Wat>ash Ave., CHICAOO 
X, 1900 



"A fitting memorial to its author.*^— 77/^ Dial 
A NO TA BLE BOOK B V THE LA TE 

FRANCIS A. WALKER 

P7-esident of the Massachusetts Institute of Technology 

DISCUSSIONS IN EDUCATION 

Edited by James Phinney Munroe. 8vo. $3.00, net. 

The author had hoped himself to collect these papers in a 
volume. They are grouped under Technological Education^ 
Manual Education^ llie Teaching of Arith?netic and College 
Problems (including College Athletics), A Valedictory appropri- 
ately closes the book. 

The Outlook : ** Space fails us here to transcribe some pas- 
sages we had marked as maxims for the times. So long as the 
reforms and improvements in our educational methods which 
General Walker advocated, not without some success, are but 
partially accomplished, will this volume of expert testimony 
deserve to be close at hand to those with whom is the respon- 
sibility of direction." 

The Dial: "A fitting memorial to its author. . . The 
breadth of his experience, as well as the natural range of his 
mind, are here reflected. The subjects dealt with are all live 
and practical. . . . He never deals with them in a narrow or 
so-called 'practical' way." 

The Boston l^anscript : "Two of his conspicuous merits 
characterize these papers, the peculiar power he possessed of 
enlisting and retaining the attention for what are commonly 
supposed to be dry and difficult subjects, and the capacity he 
had for controversy, sharp and incisive, but so candid and 
generous that it left no festering wound." 

The Review of Reviews : "A strong presentation of the 
scope and dignity of technological education, and its relations 
to other forms of culture." 

The School Review : "The scope and power of the contents 
make the work a permanent contribution to the development 
of educational thought and principle.* 

EARLIER BOOKS BY GEN. FRANCIS A. WALKER 

{Circular free,) Wages. 428 pp. l2mo. $2.00. — Money. 
550 pp. T2mo. $2.00. — Afoney in its Relations to Trade and 
Industry, 339 pp. l2mo. $1.25.- — International Bimetallism, 
297 pp. i2mo. $1.25. — Political Economy {^Advanced Course, 
537 PP- 8vo. $2.00, 7iet, — Briefer Course. 415 pp. i2mo. 
$1.20, net, — Elementary Course, 323 pp. i2mo. $1.00, net.) 

HFNRY HOI T Rt TO 29 west 23(i St., new york 

nciNtVl nULl ex \J<J. 3^8 WatasH Ave., CHICAGO 
?c, 1900 



EUHNS'S GERMAN AND SWISS SETTLEMENT g 
OF COLONIAL PENNSYLVANIA 

A Study of the So-called Pennsylvania Dutch. 

By Oscar Kuhns, Member of the Pennsylvania Society of the 
Sons of the Revolution^ of the Pennsylvania-German Society^ 
and of the Lancaster County Historical Society. 268 pp. i2mo. 
$1.50. 

"All that is best in their history is compressed into this little volume, 
and even their defenders will be surprised to learn how much romance 
there is in the story of their suiiferings in the Palatinate, and how much 
spiritual exaltation there was back of iheir emigration to America. . . . 
The author's account of the religious faith and feeling of the German 
Quakers is written with great sympathy and insight, and his apology for 
the deep-seated conservatism of the Pennsylvania Dutch is skillfully 
made." — Outlook. 

"An historical work of peculiar and capital interest. . . . A chapter 
in modern history, particularly in American history, which Americans in 
whatever part of the country cannot afford to be ignorant of. . . . The 
writer has managed with extraordinary skill to infuse into his narrative 
the constant element of personal interest, so that the whole story is trans- 
fused with the spirit of a fascinating romance."— C^/Va^i? Evening Post. 

"Ein erschopfendes Bild jener einwanderung, dasssich durch sachliche 
Ruhe und Unparteilichkeit auszeichnet und einer ausfiihrlichen Besprech- 
ung werth ist, . . . So interessant auch die Ausfuhrungen des Verfassers 
iiber die vielen Sekten sind, die theils sich hier niederlieszen, theils hier 
gebildet wurden, so konnen wir ihm darin nicht folgen." — N, i'. Staats- 
Zeitung. 

"No more exhaustive account of the origin, emigration and subsequent 
history of the early German and Swiss settlers in Pennsylvania than this 
has yet been issued, . . . The appendix concerning the change in form 
undergone by many Pennsylvania-German family names, the bibliography, 
and index contribute greatly to the interest and practical importance of 
Mr, Kuhns's valuable monograph." — Philadelphia Ledger, 

*' It is a first-rate service to the cause of American history which Osca:" 
Kuhns has rendered in his popular yet scholarly book. . . . An exceedingly 
interesting and instructive story." — Chicago Record-Herald. 

McCRACKAN'S RISE OF THE SWISS REPUBLIC 

A History. By W. D. McCkackan. Second Edition., Revised 
and Enlarged, x -4-423 pp. 8vo. $2.00. 

" This is the most convenient and serviceable book in English on Swiss 
history and development, and America has much to learn from the experi- 
ence of our sister republic." — Prof. Albert B. Hart., of Harvard. 

" It seems to me that you have happily blended the picturesque treat- 
ment which some parts of Swiss history demand, with the object of bring- 
ing out the political lesson of the last thirty or fitiy years, I trust your 
book may do much to show our people, as well as yours, how much is to 
be learned from a study of Swiss affairs." — The Right Hon. fames Bryce^ 
M.P. 

" AU things considered, this history seems to me to be fk and away the 
best Swiss history ever yet published in English." — English Historical 
Review . 

HENRY HOLT & CO. ^^ ^^i^^^%t'^^^' 



ENGLISH ROMANTICISM 

By Prof. Henry A. Beers of Yale 
2 vols. i2mo, laid paper, gilt tops 

THE EIGHTEENTH CENTURY. $2. 

Contents: The Subject Defined; The Augustans; The vSpenser- 
ians; The Landscape Poets; The Miltonic Group; The School of 
Warton; The Gothic Revival; Percy and the Ballads; Ossian; 
Thomas Chatterton; and The German Tributary. 

" The individuality of his style, its humor, its color, its delicacy 
. . . will do quite as much to continue its author's reputation as 
his scholarship. The book is the work of a man who has studied 
hard, but who has also lived." — New York Commercial Advertiser. 

'' One of the most important contributions yet made to literary 
history by an American scholar." — Outlook. 

''Remarkably penetrating and scholarly. It is a noteworthy 
book by an acknowledged authority upon a most interesting 
period." — New York Ti?nes Saturday Review. 

*' Always interesting. . . . On the whole, may be commended 
as an excellent popular treatment of the special subject of the lit- 
erary revival of mediaevalism in the eighteenth century in 
England." — Nation. 

THE NINETEENTH CENTURY. $175 net. (Postage 15c.) 

Contents: Walter Scott; Coleridge, Bowles, and the Pope Con- 
troversy; Keats, Leigh Hunt, and the Dante Revival; The Roman- 
tic School in Germany; The Romantic Movement in France; 
Diffused Romanticism in the Literature of the Nineteenth Century; 
The Pre-Raphaelites; Tendencies and Results. 

"Among the few really great contributions to the study of Anglo- 
Saxon literature yet made by American scholars. . . . Prof. Beers 
is a delightfully human student, a companion on the way, not a 
Dry-as-dust of portentous mien." — Mail and Express. 

*' Where there is need of taste in forming and realizing an im- 
pression, and play for a gift of humorous and picturesque phrase of 
expression. Prof. Beers is at his best. . . . Full of felicitous judg- 
ments and memorable sentences." — Nation. 

'* There is a large feeling of the onward sweep of events that is 
almost dramatic. ... It is in making his readers understand the 
spirit of the age that Prof. Beers excels." — Book-Buyer. 

*' Full of color, change, animation, and vivacity. The general 
romantic ' chain ' is traced with an instinct that is unerring. . . . 
He does not neglect to mention such newcomers as Hewlett, Yeats, 
and John Davidson." — Chicago Post, 

HENRY HOLT & CO. ^^ ^?4^|^rl**«» 

iz '02 



DOWDEN>S PURITAN AND ANGLICAN 

Studies in Literature. By Edward Dowden. 
341 pp. 8vo. I2.00 net, 

** He has something to say and says it with clearness. 
. . . Notably lucid and instructive. . . , Not without the 
more vivacious quality which comes from a sympathetic 
handling of personal traits." — N, Y. Tribune, 

"A notable series of appreciations bound together by a 
vital unity of subject and interest. . . . The work as a 
whole is as full of ripe judgment as it is of sound learning; 
and it is pervaded withal by a vivid personal enthusiasm 
which makes it delightful reading." — N^ation, 

*' His new book is important. . . . One may find therein 
the formative influences of early American literature." — 
Times Saturday Review. 

*' The latest volume has all the unity, clearness, and 
sympathy of his former admirable Shakespearian studies. 
. . . As detecting and expounding the deep and vital 
forces at work behind a literature of a given period, as 
pointing out salient points of resemblance as well as of 
diflierence between these forces, and as giving a moral and 
showing the tendency of the thought of that period, Prof, 
Dowden's forte is in freest play." — N, K. CommerciaL 

SELECTIONS FROM DANTE>S DIVINA COM- 
MEDIA 

Chosen, Translated, and Annotated by Richard 
James Cross. The original and translation on oppo- 
site pages. Bound in Florentine style 225 pp. 
i6mo. I2.00. 

*'The work has been executed by botR (translator and 
publisher with a taste and skill which justify the under- 
taking. The translations are in prose and adhere very 
closely to the original. While discarding all the adorn- 
ments which a metrical version might permit, and depend- 
ing solely upon the interest and import of Dante's thought, 
he has at the same time succeeded in keeping much of the 
spirit of the poem." — Nation. 

'*This is a pretty volume to the eye. The translator's 
sympathy with Dante, his elective taste, and his sense of 
rhythm in prose make his studies in the interpretation of 
the great Italian poet interesting and in the main accept- 
able. Mr. Cross's version is smooth, lucid, and luminous." 
— Literary World, 

HENRY HOLT & CO. ^^ ^^i^^%A'^^\ 

VI '01 






